The midfielder has moved to Selhurst Park on a three-year deal and plays under Ian Holloway for the second time, after achieving promotion together at Blackpool
The Scotland international follows Reading defender Adrian Mariappa to Selhurst Park on transfer deadline day, with Ian Holloway hopeful of completing further deals.
Goal revealed Palace are confident of signing Nicklas Bendtner, who arrived at the club's training ground on Monday, although the move could hinge on Arsenal being able to loan Demba Ba from Chelsea.
Bannan, meanwhile, is now due to meet up with the Scotland squad ahead of World Cup qualifiers against Belgium and Macedonia.
“I went back home to Scotland over the weekend ahead of meeting up with the international squad so I've had to travel back down but it's a great bit of news for me," Bannan told the club's official website.
“I was at Blackpool with the gaffer here when they got promotion that year and that was probably the highlight of my career so far.
“It is a big move for me to leave Villa and I would like to thank the fans there but it's a new chapter in my life now and I can't wait to get started.
“I want to get myself in the door and start training and hopefully get myself in the team. I haven't played this season and didn't much last year so I can't wait to get going.”