diff --git a/src/pip/_internal/build_env.py b/src/pip/_internal/build_env.py
index d8c7acc48..d744cc78a 100644
--- a/src/pip/_internal/build_env.py
+++ b/src/pip/_internal/build_env.py
@@ -189,8 +189,6 @@ class BuildEnvironment(object):
             args.extend(['--trusted-host', host])
         if finder.allow_all_prereleases:
             args.append('--pre')
-        if finder.process_dependency_links:
-            args.append('--process-dependency-links')
         args.append('--')
         args.extend(requirements)
         with open_spinner(message) as spinner:
diff --git a/src/pip/_internal/cli/base_command.py b/src/pip/_internal/cli/base_command.py
index 1212cd5f4..175dbadc1 100644
--- a/src/pip/_internal/cli/base_command.py
+++ b/src/pip/_internal/cli/base_command.py
@@ -296,7 +296,6 @@ class RequirementCommand(Command):
             index_urls=index_urls,
             trusted_hosts=options.trusted_hosts,
             allow_all_prereleases=options.pre,
-            process_dependency_links=options.process_dependency_links,
             session=session,
             platform=platform,
             versions=python_versions,
diff --git a/src/pip/_internal/cli/cmdoptions.py b/src/pip/_internal/cli/cmdoptions.py
index 563cd58cd..0aebf75e8 100644
--- a/src/pip/_internal/cli/cmdoptions.py
+++ b/src/pip/_internal/cli/cmdoptions.py
@@ -347,17 +347,6 @@ def trusted_host():
     )
 
 
-# Remove after 1.5
-process_dependency_links = partial(
-    Option,
-    "--process-dependency-links",
-    dest="process_dependency_links",
-    action="store_true",
-    default=False,
-    help="Enable the processing of dependency links.",
-)  # type: Callable[..., Option]
-
-
 def constraints():
     # type: () -> Option
     return Option(
@@ -773,6 +762,5 @@ index_group = {
         extra_index_url,
         no_index,
         find_links,
-        process_dependency_links,
     ]
 }  # type: Dict[str, Any]
diff --git a/src/pip/_internal/commands/list.py b/src/pip/_internal/commands/list.py
index c6eeca79e..019f85dcd 100644
--- a/src/pip/_internal/commands/list.py
+++ b/src/pip/_internal/commands/list.py
@@ -118,7 +118,6 @@ class ListCommand(Command):
             index_urls=index_urls,
             allow_all_prereleases=options.pre,
             trusted_hosts=options.trusted_hosts,
-            process_dependency_links=options.process_dependency_links,
             session=session,
         )
 
@@ -168,16 +167,8 @@ class ListCommand(Command):
             logger.debug('Ignoring indexes: %s', ','.join(index_urls))
             index_urls = []
 
-        dependency_links = []
-        for dist in packages:
-            if dist.has_metadata('dependency_links.txt'):
-                dependency_links.extend(
-                    dist.get_metadata_lines('dependency_links.txt'),
-                )
-
         with self._build_session(options) as session:
             finder = self._build_package_finder(options, index_urls, session)
-            finder.add_dependency_links(dependency_links)
 
             for dist in packages:
                 typ = 'unknown'
diff --git a/src/pip/_internal/index.py b/src/pip/_internal/index.py
index 1f2723e38..9eda3a351 100644
--- a/src/pip/_internal/index.py
+++ b/src/pip/_internal/index.py
@@ -31,7 +31,6 @@ from pip._internal.models.index import PyPI
 from pip._internal.models.link import Link
 from pip._internal.pep425tags import get_supported
 from pip._internal.utils.compat import ipaddress
-from pip._internal.utils.deprecation import deprecated
 from pip._internal.utils.logging import indent_log
 from pip._internal.utils.misc import (
     ARCHIVE_EXTENSIONS, SUPPORTED_EXTENSIONS, WHEEL_EXTENSION, normalize_path,
@@ -268,7 +267,6 @@ class PackageFinder(object):
         index_urls,  # type: List[str]
         allow_all_prereleases=False,  # type: bool
         trusted_hosts=None,  # type: Optional[Iterable[str]]
-        process_dependency_links=False,  # type: bool
         session=None,  # type: Optional[PipSession]
         format_control=None,  # type: Optional[FormatControl]
         platform=None,  # type: Optional[str]
@@ -315,7 +313,6 @@ class PackageFinder(object):
             self.find_links.append(link)
 
         self.index_urls = index_urls
-        self.dependency_links = []  # type: List[str]
 
         # These are boring links that have already been logged somehow:
         self.logged_links = set()  # type: Set[Link]
@@ -331,9 +328,6 @@ class PackageFinder(object):
         # Do we want to allow _all_ pre-releases?
         self.allow_all_prereleases = allow_all_prereleases
 
-        # Do we process dependency links?
-        self.process_dependency_links = process_dependency_links
-
         # The Session we'll use to make requests
         self.session = session
 
@@ -375,22 +369,6 @@ class PackageFinder(object):
             )
         return "\n".join(lines)
 
-    def add_dependency_links(self, links):
-        # type: (Iterable[str]) -> None
-        # FIXME: this shouldn't be global list this, it should only
-        # apply to requirements of the package that specifies the
-        # dependency_links value
-        # FIXME: also, we should track comes_from (i.e., use Link)
-        if self.process_dependency_links:
-            deprecated(
-                "Dependency Links processing has been deprecated and will be "
-                "removed in a future release.",
-                replacement="PEP 508 URL dependencies",
-                gone_in="19.0",
-                issue=4187,
-            )
-            self.dependency_links.extend(links)
-
     @staticmethod
     def _sort_locations(locations, expand_dir=False):
         # type: (Sequence[str], bool) -> Tuple[List[str], List[str]]
@@ -587,7 +565,7 @@ class PackageFinder(object):
         # type: (str) -> List[Optional[InstallationCandidate]]
         """Find all available InstallationCandidate for project_name
 
-        This checks index_urls, find_links and dependency_links.
+        This checks index_urls and find_links.
         All versions found are returned as an InstallationCandidate list.
 
         See _link_package_versions for details on which files are accepted
@@ -597,21 +575,18 @@ class PackageFinder(object):
         fl_file_loc, fl_url_loc = self._sort_locations(
             self.find_links, expand_dir=True,
         )
-        dep_file_loc, dep_url_loc = self._sort_locations(self.dependency_links)
 
         file_locations = (Link(url) for url in itertools.chain(
-            index_file_loc, fl_file_loc, dep_file_loc,
+            index_file_loc, fl_file_loc,
         ))
 
         # We trust every url that the user has given us whether it was given
-        #   via --index-url or --find-links
-        # We explicitly do not trust links that came from dependency_links
+        #   via --index-url or --find-links.
         # We want to filter out any thing which does not have a secure origin.
         url_locations = [
             link for link in itertools.chain(
                 (Link(url) for url in index_url_loc),
                 (Link(url) for url in fl_url_loc),
-                (Link(url) for url in dep_url_loc),
             )
             if self._validate_secure_origin(logger, link)
         ]
@@ -639,17 +614,6 @@ class PackageFinder(object):
                     self._package_versions(page.iter_links(), search)
                 )
 
-        dependency_versions = self._package_versions(
-            (Link(url) for url in self.dependency_links), search
-        )
-        if dependency_versions:
-            logger.debug(
-                'dependency_links found: %s',
-                ', '.join([
-                    version.location.url for version in dependency_versions
-                ])
-            )
-
         file_versions = self._package_versions(file_locations, search)
         if file_versions:
             file_versions.sort(reverse=True)
@@ -662,10 +626,7 @@ class PackageFinder(object):
             )
 
         # This is an intentional priority ordering
-        return (
-            file_versions + find_links_versions + page_versions +
-            dependency_versions
-        )
+        return file_versions + find_links_versions + page_versions
 
     def find_requirement(self, req, upgrade):
         # type: (InstallRequirement, bool) -> Optional[Link]
diff --git a/src/pip/_internal/operations/prepare.py b/src/pip/_internal/operations/prepare.py
index 23383b1af..8ec55db00 100644
--- a/src/pip/_internal/operations/prepare.py
+++ b/src/pip/_internal/operations/prepare.py
@@ -97,15 +97,9 @@ class IsWheel(DistAbstraction):
 
 class IsSDist(DistAbstraction):
 
+    # TODO: Remove 'finder' and the note in operations/check.py
     def dist(self, finder):
-        # type: (PackageFinder) -> pkg_resources.Distribution
-        dist = self.req.get_dist()
-        # FIXME: shouldn't be globally added.
-        if finder and dist.has_metadata('dependency_links.txt'):
-            finder.add_dependency_links(
-                dist.get_metadata_lines('dependency_links.txt')
-            )
-        return dist
+        return self.req.get_dist()
 
     def prep_for_dist(self, finder, build_isolation):
         # type: (PackageFinder, bool) -> None
diff --git a/src/pip/_internal/req/req_file.py b/src/pip/_internal/req/req_file.py
index e92b7968b..726f2f6a0 100644
--- a/src/pip/_internal/req/req_file.py
+++ b/src/pip/_internal/req/req_file.py
@@ -55,7 +55,6 @@ SUPPORTED_OPTIONS = [
     cmdoptions.no_binary,
     cmdoptions.only_binary,
     cmdoptions.pre,
-    cmdoptions.process_dependency_links,
     cmdoptions.trusted_host,
     cmdoptions.require_hashes,
 ]  # type: List[Callable[..., optparse.Option]]
@@ -251,8 +250,6 @@ def process_line(
             finder.find_links.append(value)
         if opts.pre:
             finder.allow_all_prereleases = True
-        if opts.process_dependency_links:
-            finder.process_dependency_links = True
         if opts.trusted_hosts:
             finder.secure_origins.extend(
                 ("*", host, "*") for host in opts.trusted_hosts)
diff --git a/src/pip/_internal/utils/outdated.py b/src/pip/_internal/utils/outdated.py
index 03360c712..37c47a4a5 100644
--- a/src/pip/_internal/utils/outdated.py
+++ b/src/pip/_internal/utils/outdated.py
@@ -127,7 +127,6 @@ def pip_version_check(session, options):
                 index_urls=[options.index_url] + options.extra_index_urls,
                 allow_all_prereleases=False,  # Explicitly set to False
                 trusted_hosts=options.trusted_hosts,
-                process_dependency_links=options.process_dependency_links,
                 session=session,
             )
             all_candidates = finder.find_all_candidates("pip")
diff --git a/src/pip/_internal/vcs/subversion.py b/src/pip/_internal/vcs/subversion.py
index 87970f1bc..1bdc9ca79 100644
--- a/src/pip/_internal/vcs/subversion.py
+++ b/src/pip/_internal/vcs/subversion.py
@@ -61,6 +61,7 @@ class Subversion(VersionControl):
         cmd_args = ['update'] + rev_options.to_args() + [dest]
         self.run_command(cmd_args)
 
+    # TODO: Remove
     def get_location(self, dist, dependency_links):
         for url in dependency_links:
             egg_fragment = Link(url).egg_fragment
diff --git a/tests/functional/test_install_reqs.py b/tests/functional/test_install_reqs.py
index bda45b107..5c56a0e12 100644
--- a/tests/functional/test_install_reqs.py
+++ b/tests/functional/test_install_reqs.py
@@ -175,8 +175,8 @@ def test_respect_order_in_requirements_file(script, data):
 
 def test_install_local_editable_with_extras(script, data):
     to_install = data.packages.join("LocalExtras")
-    res = script.pip(
-        'install', '-e', to_install + '[bar]', '--process-dependency-links',
+    res = script.pip_install_local(
+        '-e', to_install + '[bar]',
         expect_error=False,
         expect_stderr=True,
     )
diff --git a/tests/unit/test_finder.py b/tests/unit/test_finder.py
index 9f82a18a8..c8ae693dd 100644
--- a/tests/unit/test_finder.py
+++ b/tests/unit/test_finder.py
@@ -300,50 +300,6 @@ def test_finder_priority_file_over_page(data):
     assert link.url.startswith("file://")
 
 
-def test_finder_deplink():
-    """
-    Test PackageFinder with dependency links only
-    """
-    req = install_req_from_line('gmpy==1.15', None)
-    finder = PackageFinder(
-        [],
-        [],
-        process_dependency_links=True,
-        session=PipSession(),
-    )
-    finder.add_dependency_links(
-        ['https://files.pythonhosted.org/packages/source/g/gmpy/gmpy-1.15.zip']
-    )
-    link = finder.find_requirement(req, False)
-    assert link.url.startswith("https://files.pythonhosted.org/"), link
-
-
-@pytest.mark.network
-def test_finder_priority_page_over_deplink():
-    """
-    Test PackageFinder prefers page links over equivalent dependency links
-    """
-    req = install_req_from_line('pip==1.5.6', None)
-    finder = PackageFinder(
-        [],
-        ["https://pypi.org/simple/"],
-        process_dependency_links=True,
-        session=PipSession(),
-    )
-    finder.add_dependency_links([
-        'https://files.pythonhosted.org/packages/source/p/pip/pip-1.5.6.tar.gz'
-    ])
-    all_versions = finder.find_all_candidates(req.name)
-    # Check that the dependency_link is last
-    assert all_versions[-1].location.url.startswith(
-        'https://files.pythonhosted.org/'
-    )
-    link = finder.find_requirement(req, False)
-    assert link.url.startswith(
-        "https://files.pythonhosted.org/packages/3f/08/7347ca4"
-    ), link
-
-
 def test_finder_priority_nonegg_over_eggfragments():
     """Test PackageFinder prefers non-egg links over "#egg=" links"""
     req = install_req_from_line('bar==1.0', None)
diff --git a/tests/unit/test_req.py b/tests/unit/test_req.py
index 9d146e36c..32cc1b36d 100644
--- a/tests/unit/test_req.py
+++ b/tests/unit/test_req.py
@@ -82,6 +82,7 @@ class TestRequirementSet(object):
             reqset,
         )
 
+    # TODO: Update test when Python 2.7 or Python 3.4 is dropped.
     def test_environment_marker_extras(self, data):
         """
         Test that the environment marker extras are used with
diff --git a/tests/unit/test_req_file.py b/tests/unit/test_req_file.py
index bdf721794..b71ca68d0 100644
--- a/tests/unit/test_req_file.py
+++ b/tests/unit/test_req_file.py
@@ -413,11 +413,6 @@ class TestProcessLine(object):
         call = mock_parse.mock_calls[0]
         assert call[1][0] == 'http://me.com/me/reqs.txt'
 
-    def test_set_finder_process_dependency_links(self, finder):
-        list(process_line(
-            "--process-dependency-links", "file", 1, finder=finder))
-        assert finder.process_dependency_links
-
 
 class TestBreakOptionsArgs(object):
 
diff --git a/tests/unit/test_unit_outdated.py b/tests/unit/test_unit_outdated.py
index a9441a4d3..31b5a7fa3 100644
--- a/tests/unit/test_unit_outdated.py
+++ b/tests/unit/test_unit_outdated.py
@@ -50,8 +50,7 @@ def _options():
     ''' Some default options that we pass to outdated.pip_version_check '''
     return pretend.stub(
         find_links=False, extra_index_urls=[], index_url='default_url',
-        pre=False, trusted_hosts=False, process_dependency_links=False,
-        cache_dir='',
+        pre=False, trusted_hosts=False, cache_dir='',
     )