diff --git a/django/db/backends/mysql/base.py b/django/db/backends/mysql/base.py
index ea6f50ef1c7..91e0e832420 100644
--- a/django/db/backends/mysql/base.py
+++ b/django/db/backends/mysql/base.py
@@ -141,8 +141,6 @@ class DatabaseWrapper(BaseDatabaseWrapper):
         'iexact': 'LIKE %s',
         'contains': 'LIKE BINARY %s',
         'icontains': 'LIKE %s',
-        'regex': 'REGEXP BINARY %s',
-        'iregex': 'REGEXP %s',
         'gt': '> %s',
         'gte': '>= %s',
         'lt': '< %s',
diff --git a/django/db/backends/mysql/operations.py b/django/db/backends/mysql/operations.py
index e5c0c5c71b7..47e179db41e 100644
--- a/django/db/backends/mysql/operations.py
+++ b/django/db/backends/mysql/operations.py
@@ -282,3 +282,14 @@ class DatabaseOperations(BaseDatabaseOperations):
             # EXTENDED and FORMAT are mutually exclusive options.
             prefix += ' EXTENDED'
         return prefix
+
+    def regex_lookup(self, lookup_type):
+        # REGEXP BINARY doesn't work correctly in MySQL 8+ and REGEXP_LIKE
+        # doesn't exist in MySQL 5.6.
+        if self.connection.mysql_version < (8, 0, 0):
+            if lookup_type == 'regex':
+                return '%s REGEXP BINARY %s'
+            return '%s REGEXP %s'
+
+        match_option = 'c' if lookup_type == 'regex' else 'i'
+        return "REGEXP_LIKE(%%s, %%s, '%s')" % match_option
diff --git a/docs/releases/2.0.7.txt b/docs/releases/2.0.7.txt
index 4890ee2dbab..8d06deb226f 100644
--- a/docs/releases/2.0.7.txt
+++ b/docs/releases/2.0.7.txt
@@ -14,3 +14,5 @@ Bugfixes
 
 * Fixed admin check crash when using a query expression in
   ``ModelAdmin.ordering`` (:ticket:`29428`).
+
+* Fixed ``__regex`` and ``__iregex`` lookups with MySQL 8 (:ticket:`29451`).