Palace have paid an undisclosed fee for the 26-year-old, who was a substitute during United's win over Nottingham Forest on Saturday.
"There's something being built here and I really want to be a part of it," said Henderson.
"This club has got great fans and has a lot of top players who are hungry to succeed," he added.
"I'm absolutely delighted and buzzing to be here. I can't wait to get started."
Henderson has been with United since the age of 14 but never established himself as the team's first-choice keeper, going on loan spells to Stockport, Grimsby, Shrewsbury and Sheffield United, as well as Forest.
Another former Manchester United keeper, Sam Johnstone, has started the season in goal for Palace and the 30-year-old was named in the latest England squad on Thursday.
"Dean is a fantastic addition to our squad and goalkeeping unit," said Palace chairman Steve Parish. "We have been long-term admirers."
Manchester United signed Andre Onana to replace David de Gea as their first-choice keeper this summer and are set to buy Fenerbahce's Altay Bayindir for £4.3m to replace Henderson as their back-up option.
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