Henderson has been unable to displace David De Gea as Manchester United's first choice since returning from a two-year loan at Sheffield United in the summer of 2020.
Henderson made 26 appearances in all competitions for the Red Devils in the 2020/2021 season but featured just just three times across all competitions last term, with none of them coming in the Premier League.
The 25-year-old, who has one cap for England, is Forest's second summer signing after Nigeria striker Taiwo Awoniyi joined from Union Berlin.
Forest manager Steve Cooper told the club's official website: "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 join Nottingham Forest for our return to the Premier League."
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."
Henderson has a contract with Manchester United until the summer of 2025.
