The goalkeeper will spend the 2022/23 season with the two-time European champions, who were promoted back to the top flight following their play-off final victory over Huddersfield Town in May.
Henderson, 25, is a product of the club’s Academy and has been at United since the age of 14.
The former youth-team player has had significant success out on loan in the past, enjoying a range of valuable experiences at Stockport County, Grimsby Town, Shrewsbury Town and Sheffield United.
Forest begin their campaign at Newcastle United on 6 August before Premier League football returns to The City Ground with the visit of West Ham United on 13 August.