The Norway international joined Palace last year following his release from Fulham and made 14 Premier League appearances, helping them to a 10th-placed finish.
Hangeland had looked set to leave, having been included on the released list, but has put pen to paper on a new deal.
"I'm delighted to have signed with Crystal Palace for the new season," the 33-year-old told the club's official website.
"I have really enjoyed working under Alan Pardew and we have a very talented squad who are all a really good bunch of lads to be around.
"These are very exciting times at the club and I look forward to playing a part in making next year another successful one."