The 45-year-old former England, Manchester United, Inter Milan and Liverpool midfielder has agreed a one-year rolling contract at Bloomfield Road.
Following a near two-year absence from management, Ince will take charge of his son and England Under-21 winger Tom, who is Blackpool's top scorer with 17 goals in 33 games this season.
"It's great to be here," Ince told Blackpool's official website after taking his first training session at Squires Gate.
"Considering I've watched the team play for the last 14 months, it's strange sitting here as the manager, having obviously watched Blackpool as a fan as well as watching my son play.
"I'm over the moon, though, and delighted, it's great to be back on the training ground and great to be involved with, and in charge of, a great bunch of lads.
"I've worked with a lot of players and the spirit and togetherness of the lads is absolutely fantastic. I'm glad I've been given the opportunity by (Blackpool chairman) Karl Oyston."
Ince is Blackpool's third manager this season, following on from Ian Holloway and Michael Appleton.