The 23-year-old had found first-team chances harder to come by at Villa Park in recent years and will link up with Holloway for the second time, after playing under the Eagles boss during a loan-spell at Blackpool.
Bannan, who put off joining up with the Scotland squad to thrash out the terms of a three-year deal with Palace, told the club's website he was looking forward to a fresh start at Selhurst Park.
"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," he said.
"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."