The 24-year-old joined the Millers in the summer for his second loan spell with the club and scored four goals in 28 appearances this season, including a brace in the 6-1 win over Bolton Wanderers in the autumn.
Morris has now linked up with MK Dons, managed by former Canaries defender Russell Martin.
Cambridge-born Morris said: "I am over the moon.
"There were a few clubs interested in me but this was the most attractive option for me for various reasons - the team plays an attractive brand of football under the new manager and I know a few people here too.
"Me and Russ have been close for years. He was very helpful to me as a young pro coming through at Norwich.
"I have always appreciated that and now I have the opportunity to work under him – it was an opportunity I did not want to pass up on.
"The team has gone to strength to strength with some good results recently and I think this is a good place to be."