The 26-year-old goalkeeper has been with Manchester United since 2011 but has yet to properly establish himself as the first choice between the sticks.
After loan spells at Sheffield United (twice), Shrewsbury Town, Grimsby Town, and Stockport County, the England international spent last season with Nottingham Forest.
The departure of David De Gea may have provided Henderson with an opportunity at Old Trafford, but the addition of Andre Onana from Inter Milan ensured that the Englishman would continue to play second fiddle, and he has elected to go on to pursue more first-team opportunities.
According to the Telegraph, the deal to bring Henderson to Crystal Palace was finalized on Wednesday, with an official announcement expected on Thursday.
The goalkeeper has agreed to terms with the Eagles on a five-year contract and is expected to start immediately ahead of Sam Johnstone and want-away veteran Vicente Guaita.
According to the source, United is preparing to sign Altay Bayindir from Fenerbahce as Henderson’s replacement for under £4.3 million, with the Turkey international deputizing for Onana.
Henderson’s time at Manchester United comes to an end after only 29 games, 13 of which were in the Premier League and the majority in cup competitions.
He joins a Palace team that has enjoyed a strong start to the season despite the loss of Wilfried Zaha to Galatasaray in the summer.
This season, Roy Hodgson’s players have a win, a loss, and a draw from their first three Premier League games, and they knocked Plymouth out of the League Cup on Tuesday night.