Use a custom GrapeLogging formatter to get the timestamp

lib/api/api.rb

@@ -5,8 +5,8 @@ module API
     LOG_FILENAME = Rails.root.join("log", "api_json.log")
 
     use GrapeLogging::Middleware::RequestLogger,
-        logger: ::Gitlab::ApiLogger.new(LOG_FILENAME),
-        formatter: GrapeLogging::Formatters::Json.new,
+        logger: Logger.new(LOG_FILENAME),
+        formatter: Gitlab::GrapeLogging::Formatters::LogrageWithTimestamp.new,
         include: [
           GrapeLogging::Loggers::Response.new,
           GrapeLogging::Loggers::FilterParameters.new,

lib/gitlab/api_logger.rb

-module Gitlab
-  class ApiLogger < ::Logger
-    def format_message(severity, timestamp, progname, message)
-      super + "\n"
-    end
-  end
-end

lib/gitlab/grape_logging/formatters/lograge_with_timestamp.rb

+module Gitlab
+  module GrapeLogging
+    module Formatters
+      class LogrageWithTimestamp
+        def call(severity, datetime, _, data)
+          time = data.delete :time
+          attributes = {
+            time: datetime.utc.iso8601(3),
+            severity: severity,
+            duration: time[:total],
+            db: time[:db],
+            view: time[:view]
+          }.merge(data)
+          ::Lograge.formatter.call(attributes) + "\n"
+        end
+      end
+    end
+  end
+end