diff --git a/src/_pytest/mark/structures.py b/src/_pytest/mark/structures.py
index 18ebc506abb..a8caabf2910 100644
--- a/src/_pytest/mark/structures.py
+++ b/src/_pytest/mark/structures.py
@@ -2,6 +2,8 @@
 import warnings
 from collections import namedtuple
 from collections.abc import MutableMapping
+from typing import List
+from typing import Optional
 from typing import Set
 
 import attr
@@ -144,7 +146,13 @@ class Mark:
     #: keyword arguments of the mark decorator
     kwargs = attr.ib()  # Dict[str, object]
 
-    def combined_with(self, other):
+    _param_ids_from = attr.ib(type=Optional["Mark"], default=None)
+    _param_ids_generated = attr.ib(type=Optional[List[str]], default=None)
+
+    def _has_param_ids(self):
+        return "ids" in self.kwargs or len(self.args) >= 4
+
+    def combined_with(self, other: "Mark") -> "Mark":
         """
         :param other: the mark to combine with
         :type other: Mark
@@ -153,8 +161,19 @@ def combined_with(self, other):
         combines by appending args and merging the mappings
         """
         assert self.name == other.name
+
+        param_ids_from = None  # type: Optional[Mark]
+        if self.name == "parametrize":
+            if other._has_param_ids():
+                param_ids_from = other
+            elif self._has_param_ids():
+                param_ids_from = self
+
         return Mark(
-            self.name, self.args + other.args, dict(self.kwargs, **other.kwargs)
+            self.name,
+            self.args + other.args,
+            dict(self.kwargs, **other.kwargs),
+            param_ids_from=param_ids_from,
         )
 
 
diff --git a/src/_pytest/python.py b/src/_pytest/python.py
index 77954239279..956d75d1c0f 100644
--- a/src/_pytest/python.py
+++ b/src/_pytest/python.py
@@ -132,7 +132,25 @@ def pytest_generate_tests(metafunc):
     _validate_parametrize_spelling(metafunc)
 
     for marker in metafunc.definition.iter_markers(name="parametrize"):
-        metafunc.parametrize(*marker.args, **marker.kwargs)
+        args, kwargs = marker.args, marker.kwargs
+        if marker._param_ids_from:
+            ids = marker._param_ids_from._param_ids_generated
+            if ids is None:
+                save_ids = True
+            else:
+                save_ids = False
+                if len(args) > 3:
+                    args = args.copy()
+                    args[3] = ids
+                else:
+                    assert "ids" in kwargs
+                    kwargs = kwargs.copy()
+                    kwargs["ids"] = ids
+
+        new_ids = metafunc.parametrize(*args, **kwargs)
+
+        if marker._param_ids_from and save_ids:
+            object.__setattr__(marker._param_ids_from, "_param_ids_generated", new_ids)
 
 
 def pytest_configure(config):
@@ -1024,6 +1042,7 @@ def parametrize(self, argnames, argvalues, indirect=False, ids=None, scope=None)
                 )
                 newcalls.append(newcallspec)
         self._calls = newcalls
+        return ids
 
     def _resolve_arg_ids(self, argnames, ids, parameters, item):
         """Resolves the actual ids for the given argnames, based on the ``ids`` parameter given
diff --git a/testing/python/metafunc.py b/testing/python/metafunc.py
index 1d8e90002e6..6e88e2223f1 100644
--- a/testing/python/metafunc.py
+++ b/testing/python/metafunc.py
@@ -1849,12 +1849,12 @@ def test_converted_to_str(a, b):
         """
         )
         result = testdir.runpytest("-vv", "-s")
-        result.stdout.fnmatch_lines_random(  # random for py35.
+        result.stdout.fnmatch_lines(
             [
                 "test_parametrize_iterator.py::test1[param0] PASSED",
                 "test_parametrize_iterator.py::test1[param1] PASSED",
-                "test_parametrize_iterator.py::test2[param2] PASSED",
-                "test_parametrize_iterator.py::test2[param3] PASSED",
+                "test_parametrize_iterator.py::test2[param0] PASSED",
+                "test_parametrize_iterator.py::test2[param1] PASSED",
                 "test_parametrize_iterator.py::test_converted_to_str[0] PASSED",
                 "test_parametrize_iterator.py::test_converted_to_str[1] PASSED",
                 "*= 6 passed in *",