The 37-year-old was granted permission to speak to Rovers on Thursday and arrives on the back of a two-month spell at Blackpool.
Appleton steps in with the club in 13th spot and five points away from the play-off places after Henning Berg was sacked last month having been in charge for just 10 games.
The former Portsmouth boss will be joined by assistant Ashley Westwood and will have had mixed emotions on Friday night when his side failed to capitalise on an early penalty in a 1-1 draw at Wolves.
"I am delighted to be joining such an historic club," Appleton said. "This is a fantastic opportunity for me and I am excited about the challenge we have ahead of us.
"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."
Appleton and Westwood will take up their posts on Monday with Gary Bowyer and Terry McPhillips looking after the team for the final time on Friday night. match.
Ahead of kick-off, Bowyer told Sky Sports: "It's business as usual. Michael called me this evening and wished the lads all the best."
Appleton won two and drew seven of his 11 Championship games in charge of Blackpool, who lie 14th in the standings and one point and one place behind Blackburn.
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."
The match at Molineux had new Wolves boss Dean Saunders taking charge of his first home game after replacing Stale Solbakken, sacked in the aftermath of Saturday's FA Cup exit at the hands of non-league Luton.
Appleton, whose playing career included spells at Manchester United and Preston, began the season in charge of League One Portsmouth and is the third Blackburn boss this season.
Steve Kean began the current campaign at the helm but resigned in September after 21 months in charge before being replaced by Berg.