The Scotland midfielder, whose last Villa appearance was in March, follows deadline-day signings Jack Hunt and Adrian Mariappa to Selhurst Park.
He told Sky Sports News: "I'm proud, obviously. It's been a long day, but now I'm a Crystal Palace player I'm very happy.
"The season's been started now for a couple of weeks and I've not featured at Villa. It's perfect for me, really, staying in the Premier League and I'll do the best I can.
"I played a lot of games last season but the gaffer at Villa has obviously decided to go another way. You can't complain - some managers like you, some don't."
The move reunites Bannan with Ian Holloway, his manager during a loan spell at Blackpool several years ago.
"I worked with him at Blackpool, and that was probably the highlight of my career so far. We got promoted to the Premier League and he was really good, so to be working under him again is brilliant."
Palace continue to chase new signings before the 11pm deadline, and Arsenal striker Nicklas Bendtner was briefly at the club's Beckenham training ground in the early afternoon.
Sky sources understand a deal could yet happen if Arsenal, who are interested in Chelsea's Demba Ba, can sign a striker.