The 20-year-old came through the Reds academy but failed to feature for the first team.
He is the son of former Blackburn and Preston defender Mick Rathbone and is the third summer arrival at Spotland.
"When I found out I was leaving Manchester United, I spoke to my coach about potential clubs," he said.
"He told me that Rochdale have great people and that it was a great club to come and play football at.
"When I met with the manager (Keith Hill) he told me that I'd have to come in and prove myself but if I was doing well then I'd get my chance. That's all I really want."
Find all the latest football transfers on our dedicated page.
League One side Rochdale have signed midfielder Oliver Rathbone on a one-year contract after his release by Manchester United.