The Athletic reports that the 26-year-old will join the London club for about £15 million plus £5 million in add-ons.
Henderson has been linked with a transfer away from Manchester United for several weeks.
At this stage of his career, the 26-year-old requires regular playing time, something he is unlikely to get at Manchester United.
Last season, he was on loan at Nottingham Forest, and he previously impressed during a loan spell at Sheffield United. There is little doubt that the 26-year-old is capable of starting in the Premier League on a regular basis, and a move to Crystal Palace might give him with the opportunities he requires.
In the coming months, Henderson will try to establish himself as a crucial player for Crystal Palace and force his way into the England squad.
Manchester United signed Andre Onana earlier this summer, and they are reportedly close to signing Altay Bayindir from Fenerbahce as well. Henderson would have been the club’s third-choice keeper, therefore it makes sense for him to leave.
Manchester United will be able to bring in their own signings thanks to the rumored £20 million deal. The Red Devils could benefit from a strong central defender as well as some depth in the central midfield.