The centre-half has rejected interest from elsewhere to commit to Palace, who this month broke their transfer record to sign Yohan Cabaye from Paris Saint-Germain.
Dann is one of several Palace players to sign a new deal in recent weeks, following on from Jason Puncheon, Julian Speroni and James McArthur among others.
He told the club website: “I’m over the moon to sign a new deal and I’m looking forward to my future here. We’re all going in the right direction and hopefully we can build on last year’s position.
“There was some interest from other clubs over the summer so I spoke to the chairman and the manager about their plans for the future.
“After hearing what they had to say, and with all the other lads signing, I knew I was at the right club so I wanted to commit my future to Palace and aim for a top-eight finish this season.
“The manager and the chairman were a big influence; the gaffer made it clear last season that there was no way I was leaving and I didn’t want to. I’m delighted to get everything signed and look forward to the coming years.
“We’re showing a lot of ambition and we’re looking to push on. Everyone wants to be a part of that by signing up for longer contracts. It’s an exciting time for us.
“Cabaye was brilliant when he was over here playing for Newcastle and did the same at PSG. He’s obviously a top player and for Palace to attract a player like that just shows where we want to be.”