The former Birmingham City defender leaves Blackburn to become Tony Pulis's third signing of deadline day, following in the footsteps of Jason Puncheon and Wayne Hennessey
Dann, a former England Under-21s international, has penned a three-and-a-half-year deal at Selhurst Park.
He becomes Palace's third signing on transfer deadline day, in a busy night for the Premier League side.
On completing his move, former Birmingham City centre-half Dann said: "It's been a long day and a long transfer window with a lot of speculation, so it's nice to finally put pen to paper and get it done. I'm looking forward to the next three and a half years.
"Any professional footballer will tell you that they want to be in the Premier League.
"It's something I've done before and really enjoyed, and having the opportunity to come and play here for the next couple of years, do well and help the team - it's something I really wanted to do and I'm glad that it's all gone through."
Goalkeeper Wayne Hennessey had already arrived from Wolves, with Jason Puncheon joining the club on a permanent basis after a spell on loan from Southampton.
Dann has previously played in the Premier League with Birmingham City, as well as Rovers, but suffered relegation with both of those clubs.
He made over 100 appearances for Gary Bowyer's side but now links up with Tony Pulis, arriving with the Eagles four points above the relegation places.
The Eagles will need to recover from their busy transfer period quickly with a tough task away to Arsenal on Sunday.