The 21-year-old’s move to Old Trafford ends a long-running transfer pursuit that started in the summer of 2020.
Sancho’s contract contains the option for a further year and he becomes Ole Gunnar Solskjaer’s first signing of the summer.
Sancho joined Borussia Dortmund from Manchester City in the summer of 2017 and he scored 50 goals and provided 57 assists in 137 appearances, winning the DFB-Pokal in his final season at the club.
"I'll always be grateful to Dortmund for giving me the opportunity to play first-team football, although I always knew that I would return to England one day," Sancho told United's official website.
"The chance to join Manchester United is a dream come true and I just cannot wait to perform in the Premier League.
"This is a young and exciting squad and I know, together, we can develop into something special to bring the success that the fans deserve.
"I am looking forward to working with the manager and his coaching team to further develop my game."
Solskjaer added: "Jadon epitomises the type of player I want to bring to the club, he is a forward player in the best traditions of Manchester United.
"He will form an integral part of my squad for years to come and we look forward to seeing him blossom.
"His goals and assists records speak for themselves and he will also bring tremendous pace, flair and creativity to the team."
Sancho has won 23 caps for the England national team and was part of the squad that finished runners up at EURO 2020.
