The 37-year-old, who succeeds Henning Berg, will be joined at Ewood Park by assistant Ashley Westwood.
After a day of discussions with Blackpool FC, Rovers were granted permission to speak to the highly-rated duo on Thursday night.
They arrived at Ewood on Friday morning, accompanied by their lawyer, before putting pen-to-paper on two-and-a-half-year deals.
Rovers’ managing director Derek Shaw said: “We are delighted to welcome both Michael and Ashley to the football club. They are both highly regarded within the game and we are confident that they have the drive and ambition to take this club forward. We will do everything in our powers to support them in our quest to make an instant return to the Premier League.”
A former Manchester United trainee, Appleton had spells at Preston North End and West Bromwich Albion, before beginning his coaching career with the Baggies.
After successful coaching roles at the club, he became assistant head coach to Roberto Di Matteo and later Roy Hodgson, before taking up the reins at Portsmouth.
Twelve months after joining the south-coast club, Blackpool came calling in November 2012. Appleton lost just two of his 12 games in charge of the Seasiders, with his last victory coming against Rovers in mid-December.
The new Rovers manager said: “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. 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.”
Gary Bowyer and Terry McPhillips will remain in charge for tonight’s game against Wolves, with Appleton and Westwood assuming their new roles next week.