The 26-year-old goalkeeper, who is having a medical on Thursday, will initially cost £15m, with a further £5m payable in add-ons, and will sign a five-year contract at Selhurst Park.
Henderson is expected to compete with Sam Johnstone to become Roy Hodgson’s No1.
Vicente Guaita, 36, is expected to leave after falling out with Hodgson. He has been accused of “refusing to play” by the manager, but sources close to the player deny that.
Palace have already signed midfielder Jefferson Lerma on a free transfer and forward Matheus Franca in a £17.25m deal from Flamengo, but are expected to be active in the last few hours of the transfer window.
They want a replacement for Wilfried Zaha, who left on a free transfer to join Galatasaray last month. Leicester striker Kelechi Iheanacho is the primary target, with Paris Saint-Germain’s Hugo Ekitike also being considered.
Jean-Philippe Mateta was thought to be on his way out, but is now in talks over a new deal.