The 36-year-old has agreed terms on a one-year rolling contract to succeed Ian Holloway, who left last weekend to take over at Championship leaders Crystal Palace.
Appleton, whose playing career was curtailed by a serious knee injury, was the only man from a shortlist of five men interviewed by Blackpool chairman Karl Oyston.
Appleton was assistant boss to Roberto Di Matteo and Roy Hodgson at West Brom before joining financially-stricken Portsmouth last year.
Ashley Westwood has also left Fratton Park after being named as first team coach at Blackpool, while Steve Thompson will continue in his role as assistant manager.
"Getting the opportunity to come to a club that has had a lot of success over previous seasons is a big part of wanting to be here," said Appleton.
"I'm just desperate to meet the players now and crack on with the job.
"As a new manager coming in you want to bring a few ideas to the new football club and the team, but I think they've got to be small steps in doing that because if it's not broken then don't mend it, just tweak it a little bit."
Meanwhile, Portsmouth have announced that Guy Whittingham will take temporary charge of the first team for their trip to Bury on Saturday.