The 37-year old has departed Bloomfield Road after just 11 matches in charge following his replacement of Ian Holloway and has signed a two-and-a-half-year deal with Rovers.
"I am delighted to be joining such an historic club. This is a fantastic opportunity for me and I am excited about the challenge we have ahead of us," read a statement from Appleton.
"I can't wait to start working with what is a very talented group of players.
"I'd like to thank everyone at Blackpool for their efforts during my time there and the chairman for allowing me to come here. I wish them all the best for the future."