"Everyone wanted to know whether I was going back to West Brom or not but I have decided to stay at Manchester United," Richardson told Sky Sports News.
"It was flattering to have the choice. I did well at West Brom and I enjoyed my time there.
"I owe Bryan Robson a lot because he took a gamble on me when I didn't have a great deal of experience.
"I know he wanted me to go back but I want to make it at Manchester United and be a Manchester United player. Hopefully I can do that this season."