diff --git a/lib/api/helpers/internal_helpers.rb b/lib/api/helpers/internal_helpers.rb
index 4c0db4d42b1..4b3c473b0bb 100644
--- a/lib/api/helpers/internal_helpers.rb
+++ b/lib/api/helpers/internal_helpers.rb
@@ -36,6 +36,18 @@ module API
         {}
       end
 
+      def fix_git_env_repository_paths(env, repository_path)
+        if obj_dir_relative = env['GIT_OBJECT_DIRECTORY_RELATIVE'].presence
+          env['GIT_OBJECT_DIRECTORY'] = File.join(repository_path, obj_dir_relative)
+        end
+
+        if alt_obj_dirs_relative = env['GIT_ALTERNATE_OBJECT_DIRECTORIES_RELATIVE'].presence
+          env['GIT_ALTERNATE_OBJECT_DIRECTORIES'] = alt_obj_dirs_relative.map { |dir| File.join(repository_path, dir) }
+        end
+
+        env
+      end
+
       def log_user_activity(actor)
         commands = Gitlab::GitAccess::DOWNLOAD_COMMANDS
 
diff --git a/lib/api/internal.rb b/lib/api/internal.rb
index 6e78ac2c903..451121a4cea 100644
--- a/lib/api/internal.rb
+++ b/lib/api/internal.rb
@@ -19,7 +19,9 @@ module API
         status 200
 
         # Stores some Git-specific env thread-safely
-        Gitlab::Git::Env.set(parse_env)
+        env = parse_env
+        env = fix_git_env_repository_paths(env, repository_path) if project
+        Gitlab::Git::Env.set(env)
 
         actor =
           if params[:key_id]
diff --git a/spec/requests/api/internal_spec.rb b/spec/requests/api/internal_spec.rb
index d919899282d..34ecdd1e164 100644
--- a/spec/requests/api/internal_spec.rb
+++ b/spec/requests/api/internal_spec.rb
@@ -203,18 +203,44 @@ describe API::Internal do
       end
 
       context 'with env passed as a JSON' do
-        it 'sets env in RequestStore' do
-          expect(Gitlab::Git::Env).to receive(:set).with({
-            'GIT_OBJECT_DIRECTORY' => 'foo',
-            'GIT_ALTERNATE_OBJECT_DIRECTORIES' => 'bar'
-          })
+        context 'when relative path envs are not set' do
+          it 'sets env in RequestStore' do
+            expect(Gitlab::Git::Env).to receive(:set).with({
+              'GIT_OBJECT_DIRECTORY' => 'foo',
+              'GIT_ALTERNATE_OBJECT_DIRECTORIES' => 'bar'
+            })
 
-          push(key, project.wiki, env: {
-            GIT_OBJECT_DIRECTORY: 'foo',
-            GIT_ALTERNATE_OBJECT_DIRECTORIES: 'bar'
-          }.to_json)
+            push(key, project.wiki, env: {
+              GIT_OBJECT_DIRECTORY: 'foo',
+              GIT_ALTERNATE_OBJECT_DIRECTORIES: 'bar'
+            }.to_json)
 
-          expect(response).to have_gitlab_http_status(200)
+            expect(response).to have_gitlab_http_status(200)
+          end
+        end
+
+        context 'when relative path envs are set' do
+          it 'sets env in RequestStore' do
+            obj_dir_relative = './objects'
+            alt_obj_dirs_relative = ['./alt-objects-1', './alt-objects-2']
+            repo_path = project.wiki.repository.path_to_repo
+
+            expect(Gitlab::Git::Env).to receive(:set).with({
+              'GIT_OBJECT_DIRECTORY' => File.join(repo_path, obj_dir_relative),
+              'GIT_ALTERNATE_OBJECT_DIRECTORIES' => alt_obj_dirs_relative.map { |d| File.join(repo_path, d) },
+              'GIT_OBJECT_DIRECTORY_RELATIVE' => obj_dir_relative,
+              'GIT_ALTERNATE_OBJECT_DIRECTORIES_RELATIVE' => alt_obj_dirs_relative
+            })
+
+            push(key, project.wiki, env: {
+              GIT_OBJECT_DIRECTORY: 'foo',
+              GIT_ALTERNATE_OBJECT_DIRECTORIES: 'bar',
+              GIT_OBJECT_DIRECTORY_RELATIVE: obj_dir_relative,
+              GIT_ALTERNATE_OBJECT_DIRECTORIES_RELATIVE: alt_obj_dirs_relative
+            }.to_json)
+
+            expect(response).to have_gitlab_http_status(200)
+          end
         end
       end