The right-back, who was offered a new deal at stadium:mk, will sign a two-year deal with the Pirates on July 1.
"I have played against Bristol Rovers over the years and they have always been a good team to play against and a good footballing side, so I'm excited to join," Regan told Rovers' official website.
"I have spoken to both Paul (Trollope) and Lennie (Lawrence), and I was impressed with what they had to say to me, and they were a big part of the reason I decided to come here.
"I think consistency is the key in this league. If we are consistent all season, there is a very good chance we will make the play-offs or go up."