diff --git a/news/5780.bugfix b/news/5780.bugfix
new file mode 100644
index 00000000000..c9aa72053cf
--- /dev/null
+++ b/news/5780.bugfix
@@ -0,0 +1 @@
+Re-install PEP 508 dependencies when the URL changes.
diff --git a/news/6402.bugfix b/news/6402.bugfix
new file mode 100644
index 00000000000..c9aa72053cf
--- /dev/null
+++ b/news/6402.bugfix
@@ -0,0 +1 @@
+Re-install PEP 508 dependencies when the URL changes.
diff --git a/src/pip/_internal/req/constructors.py b/src/pip/_internal/req/constructors.py
index 7e57f22f73b..fe6300cf216 100644
--- a/src/pip/_internal/req/constructors.py
+++ b/src/pip/_internal/req/constructors.py
@@ -434,6 +434,21 @@ def install_req_from_req_string(
             "{} depends on {} ".format(comes_from.name, req)
         )
 
+    if req.url:
+        # Create an InstallRequirement for a wheel-like PEP 508 URL with the
+        # same behavior as 'pip install req.url'
+        parts = parse_req_from_line(req.url, None)
+        link = Link(req.url)
+        if link.is_wheel:
+            return InstallRequirement(
+                parts.requirement,
+                comes_from=comes_from,
+                link=parts.link,
+                markers=parts.markers,
+                use_pep517=use_pep517,
+                isolated=isolated,
+                extras=req.extras,
+            )
     return InstallRequirement(
         req, comes_from, isolated=isolated, use_pep517=use_pep517
     )
diff --git a/tests/functional/test_install.py b/tests/functional/test_install.py
index a4bacfe9447..4d03ced5be2 100644
--- a/tests/functional/test_install.py
+++ b/tests/functional/test_install.py
@@ -1592,6 +1592,37 @@ def test_install_pep508_with_url_in_install_requires(script):
     assert "Successfully installed packaging-15.3" in str(res), str(res)
 
 
+def test_install_pep508_with_url_in_install_requires_url_change_wheel(script):
+    dep_v1_path = create_basic_wheel_for_package(
+        script, name='dep', version='1.0',
+    )
+    dep_v2_path = create_basic_wheel_for_package(
+        script, name='dep', version='2.0',
+    )
+
+    pkga_path = create_basic_wheel_for_package(
+        script, name='pkga', version='1.0',
+        depends=['dep@' + path_to_url(dep_v1_path)],
+    )
+    res = script.pip('install', pkga_path)
+    assert "Successfully installed dep-1.0" in str(res), str(res)
+
+    pkga_path.unlink()
+
+    # Updating the URL to the dependency installs the updated dependency
+    pkga_path = create_basic_wheel_for_package(
+        script, name='pkga', version='2.0',
+        depends=['dep@' + path_to_url(dep_v2_path)],
+    )
+    res = script.pip('install', pkga_path)
+    assert "Successfully installed dep-2.0" in str(res), str(res)
+
+    res = script.pip('install', pkga_path)
+    # pip can determine the version from a wheel's filename, so the
+    # dependency is not reinstalled if the URL doesn't change
+    assert "Requirement already satisfied: dep==2.0" in str(res), str(res)
+
+
 @pytest.mark.network
 @pytest.mark.parametrize('index', (PyPI.simple_url, TestPyPI.simple_url))
 def test_install_from_test_pypi_with_ext_url_dep_is_blocked(script, index):
diff --git a/tests/unit/test_req_install.py b/tests/unit/test_req_install.py
index c3482d5360a..ef0ab68858a 100644
--- a/tests/unit/test_req_install.py
+++ b/tests/unit/test_req_install.py
@@ -78,7 +78,7 @@ def test_install_req_from_string_without_comes_from(self):
 
         assert isinstance(install_req, InstallRequirement)
         assert install_req.link.url == wheel_url
-        assert install_req.req.url == wheel_url
+        assert install_req.req.url is None
         assert install_req.comes_from is None
         assert install_req.is_wheel
 
@@ -106,5 +106,47 @@ def test_install_req_from_string_with_comes_from_without_link(self):
         assert isinstance(install_req, InstallRequirement)
         assert install_req.comes_from.link is None
         assert install_req.link.url == wheel_url
-        assert install_req.req.url == wheel_url
+        assert install_req.req.url is None
         assert install_req.is_wheel
+
+    @pytest.mark.parametrize("use_pep517", [None, True, False])
+    def test_install_req_from_string_pep508_url_wheel(self, use_pep517):
+        """
+        install_req_from_string parses the version from PEP 508 URLs that point
+        to wheels so that updating the URL reinstalls the package.
+        """
+        wheel_url = ("https://download.pytorch.org/whl/cu90/"
+                     "torch-1.0.0-cp36-cp36m-win_amd64.whl")
+        install_str = "torch@ " + wheel_url
+        install_req = install_req_from_req_string(
+            install_str, use_pep517=use_pep517
+        )
+
+        assert isinstance(install_req, InstallRequirement)
+        assert str(install_req.req) == "torch==1.0.0"
+        assert install_req.link.url == wheel_url
+        assert install_req.is_wheel
+        assert install_req.use_pep517 == use_pep517
+
+    @pytest.mark.parametrize("use_pep517", [None, True, False])
+    def test_install_req_from_string_pep508_url_wheel_extras(self, use_pep517):
+        """
+        install_req_from_string parses the version and extras from PEP 508 URLs
+        that point to wheels so that updating the URL reinstalls the package.
+        """
+        wheel_url = (
+            "https://files.pythonhosted.org/packages/51/bd/"
+            "23c926cd341ea6b7dd0b2a00aba99ae0f828be89d72b2190f27c11d4b7fb/"
+            "requests-2.22.0-py2.py3-none-any.whl"
+        )
+        install_str = "requests[security] @ " + wheel_url
+        install_req = install_req_from_req_string(
+            install_str, use_pep517=use_pep517
+        )
+
+        assert isinstance(install_req, InstallRequirement)
+        assert str(install_req.req) == "requests==2.22.0"
+        assert install_req.link.url == wheel_url
+        assert install_req.is_wheel
+        assert install_req.use_pep517 == use_pep517
+        assert install_req.extras == {"security"}