The 33-year-old left Fulham at the end of last season following their relegation from the Premier League after spending six-and-a-half years at Craven Cottage.
The six-foot, four-inch, central defender played more than 200 games for the Cottagers and will join manager Tony Pulis at Palace for the forthcoming season.
After passing his medical in London, Hangeland told Sky Sports News: "It's been a long morning and I am obviously delighted to sign the contract.
"We had training after the medical and I am extremely happy to be here. It's been a long day, but a great day.
"I've done my homework on Palace, obviously I played against them last year and watched them play and they looked like an incredibly strong team.
"Everyone said that it's a club which is up-and-coming with a great bunch of lads with a good manager who organises the team well and it's in London which is convenient for me. So I am delighted to be here and I cannot wait to get going."
Earlier, the Norway international told the club's official website: "I look forward to helping out and doing the best I can for Crystal Palace.
"I'm quite old school as a player, I just want to be part of a good group of players, working for a good manager, working really hard and driving something in the right direction.
"Palace is a traditional club with a big following. I thought the atmosphere here was fantastic and obviously the fans had a lot to be happy about come the end of the season.”
And Palace chairman Steve Parish insists Hangeland will not be the last arrival at Selhurst Park during the transfer window.
"This is a statement of intent," he told Sky Sports News. "It's great that he's agreed to come to this club so it's exciting times for everyone.
"But we need to do a bit more. We know that. We are probably a little bit behind where we want to be. I'm going to see the manager now and we'll find out what else we can do.
"But along with Fraizer Campbell, Brede's a good one. He's played in the division for a long time and he knows what it's all about. He's fit and raring to go and we are excited to have him."
Hangeland becomes the third new signing at Selhurst Park following the arrivals of Campbell and goalkeeper Chris Kettings.