diff --git a/django/db/migrations/autodetector.py b/django/db/migrations/autodetector.py
index 083351a6f1..f8ec49ab0a 100644
--- a/django/db/migrations/autodetector.py
+++ b/django/db/migrations/autodetector.py
@@ -188,15 +188,26 @@ class MigrationAutodetector(object):
                     continue
                 # You can't just add NOT NULL fields with no default
                 if not field.null and not field.has_default():
+                    field = field.clone()
                     field.default = self.questioner.ask_not_null_addition(field_name, model_name)
-                self.add_to_migration(
-                    app_label,
-                    operations.AddField(
-                        model_name=model_name,
-                        name=field_name,
-                        field=field,
+                    self.add_to_migration(
+                        app_label,
+                        operations.AddField(
+                            model_name=model_name,
+                            name=field_name,
+                            field=field,
+                            preserve_default=False,
+                        )
+                    )
+                else:
+                    self.add_to_migration(
+                        app_label,
+                        operations.AddField(
+                            model_name=model_name,
+                            name=field_name,
+                            field=field,
+                        )
                     )
-                )
             # Old fields
             for field_name in old_field_names - new_field_names:
                 self.add_to_migration(
@@ -434,7 +445,8 @@ class InteractiveMigrationQuestioner(MigrationQuestioner):
         "Adding a NOT NULL field to a model"
         choice = self._choice_input(
             "You are trying to add a non-nullable field '%s' to %s without a default;\n" % (field_name, model_name) +
-            "this is not possible. Please select a fix:",
+            "we can't do that (the database needs something to populate existing rows).\n" +
+            "Please select a fix:",
             [
                 "Provide a one-off default now (will be set on all existing rows)",
                 "Quit, and let me add a default in models.py",
diff --git a/django/db/migrations/operations/fields.py b/django/db/migrations/operations/fields.py
index b609110f85..c5f0bd1e2b 100644
--- a/django/db/migrations/operations/fields.py
+++ b/django/db/migrations/operations/fields.py
@@ -1,4 +1,5 @@
 from django.db import router
+from django.db.models.fields import NOT_PROVIDED
 from .base import Operation
 
 
@@ -7,13 +8,20 @@ class AddField(Operation):
     Adds a field to a model.
     """
 
-    def __init__(self, model_name, name, field):
+    def __init__(self, model_name, name, field, preserve_default=True):
         self.model_name = model_name
         self.name = name
         self.field = field
+        self.preserve_default = preserve_default
 
     def state_forwards(self, app_label, state):
-        state.models[app_label, self.model_name.lower()].fields.append((self.name, self.field))
+        # If preserve default is off, don't use the default for future state
+        if not self.preserve_default:
+            field = self.field.clone()
+            field.default = NOT_PROVIDED
+        else:
+            field = self.field
+        state.models[app_label, self.model_name.lower()].fields.append((self.name, field))
 
     def database_forwards(self, app_label, schema_editor, from_state, to_state):
         from_model = from_state.render().get_model(app_label, self.model_name)
diff --git a/tests/migrations/test_operations.py b/tests/migrations/test_operations.py
index fb38605030..2dea14b445 100644
--- a/tests/migrations/test_operations.py
+++ b/tests/migrations/test_operations.py
@@ -1,4 +1,5 @@
 from django.db import connection, models, migrations, router
+from django.db.models.fields import NOT_PROVIDED
 from django.db.transaction import atomic
 from django.db.utils import IntegrityError
 from django.db.migrations.state import ProjectState
@@ -130,10 +131,19 @@ class OperationTests(MigrationTestBase):
         """
         project_state = self.set_up_test_model("test_adfl")
         # Test the state alteration
-        operation = migrations.AddField("Pony", "height", models.FloatField(null=True))
+        operation = migrations.AddField(
+            "Pony",
+            "height",
+            models.FloatField(null=True, default=5),
+        )
         new_state = project_state.clone()
         operation.state_forwards("test_adfl", new_state)
         self.assertEqual(len(new_state.models["test_adfl", "pony"].fields), 4)
+        field = [
+            f for n, f in new_state.models["test_adfl", "pony"].fields
+            if n == "height"
+        ][0]
+        self.assertEqual(field.default, 5)
         # Test the database alteration
         self.assertColumnNotExists("test_adfl_pony", "height")
         with connection.schema_editor() as editor:
@@ -144,6 +154,28 @@ class OperationTests(MigrationTestBase):
             operation.database_backwards("test_adfl", editor, new_state, project_state)
         self.assertColumnNotExists("test_adfl_pony", "height")
 
+    def test_add_field_preserve_default(self):
+        """
+        Tests the AddField operation's state alteration
+        when preserve_default = False.
+        """
+        project_state = self.set_up_test_model("test_adflpd")
+        # Test the state alteration
+        operation = migrations.AddField(
+            "Pony",
+            "height",
+            models.FloatField(null=True, default=4),
+            preserve_default = False,
+        )
+        new_state = project_state.clone()
+        operation.state_forwards("test_adflpd", new_state)
+        self.assertEqual(len(new_state.models["test_adflpd", "pony"].fields), 4)
+        field = [
+            f for n, f in new_state.models["test_adflpd", "pony"].fields
+            if n == "height"
+        ][0]
+        self.assertEqual(field.default, NOT_PROVIDED)
+
     def test_add_field_m2m(self):
         """
         Tests the AddField operation with a ManyToManyField.