Henderson has been with the Red Devils since the age of 14 and has 49 top-flight appearances to his name but has found himself largely acting as understudy to David de Gea at the club.
The 25-year-old previously enjoyed two loan spells with Sheffield United, helping the Blades to promotion from the Championship in 2018-2019 and earning international recognition with the Three Lions in an impressive 2019-2020 campaign.
Speaking to Forest's official website, Henderson said: "I'm absolutely delighted to be joining such a fantastic club with an amazing set of fans and a wonderful history.
"I want to thank the manager and owners at Nottingham Forest for the great opportunity to play for this club in their first season back in the Premier League. I'm really excited to work with everyone at the club from the manager, players and goalkeeper coach Danny Alcock.
"Finally, just a massive thank you to the fans for the welcome I have received and I can't wait to celebrate some brilliant moments together this coming season."
Forest head coach Steve Cooper added: "Dean is a top-class goalkeeper and he's hungry for more opportunities to play and to continue to prove himself at the highest level.
"He's played multiple times in the Premier League but has also experienced the Champions League and international football.
"Again, Dean is someone who has attracted a lot of interest from other clubs and we're delighted that he has chosen to Nottingham Forest for our return to the Premier League."
Henderson is the second arrival of the window for Forest, with forward Taiwo Awoniyi having joined from Union Berlin.
Forest defeated Huddersfield Town in May's Championship play-off final to earn promotion back to the Premier League for the first time since 1999.
Cooper's side starts the campaign at Newcastle United on 7 August (AEDT).