The 22-year-old midfielder joined Stoke in 2009 after progressing through the ranks at Crewe Alexandra, but failed to make a first-team appearance for the Potters.
Lund has said that he needed little persuasion to move to Spotland.
"I spoke to the manager (Keith Hill) yesterday and I liked his plans for the club," Lund told Rochdale's official website.
"As soon as I spoke to him I realised that we could have a good relationship working together. His plans for the club are good and I want to take that forward do well for the club.
"I saw Rochdale play a couple of times last season and I like the way he plays football and the style of it, I think it will suit the way I play."
Lund spent time on loan at Bristol Rovers and Southend United last season.