The 23-year-old spent two seasons on loan at Sheffield United, helping them earn promotion from the second tier Championship in the 2018-19 campaign before keeping 13 clean sheets in the Premier League last season.
Financial details of the contract were not disclosed but British media reported Henderson will earn about 120,000 pounds per week at United.
"The faith that the manager (Ole Gunnar Solskjaer) and the club have shown in me with this contract means a lot to me," Henderson told the club website here.
“The goalkeeping department at United is excellent; there are three top-level goalkeepers who have achieved so much in the game and I look forward to working with the group.”