The Denmark international was a free agent after leaving Brentford, where he spent six months on his return to active football following a cardiac arrest at last summer's European championships.
Eriksen made 11 appearances for Brentford in the second half of the 2021/2022 season, scoring one goal and providing four assists to help the Bees maintain their top flight status.
Eriksen is new Manchester United manager Erik Ten Hag's second summer signing after Tyrell Malacia joined from Feyenoord.
United were in need of reinforcements in midfield following the exits of Paul Pogba, Nemanja Matic and Juan Mata.
Eriksen has signed a three-year contract at Old Trafford.
Eriksen said of his move to United: “Manchester United is a special club, and I cannot wait to get started. I have had the privilege of playing at Old Trafford many times but to do it in the red shirt of United will be an amazing feeling.
“I have seen Erik’s work at Ajax and know the level of detail and preparation that he and his staff put into every day. It is clear that he is a fantastic coach.
“Having spoken with him and learned more about his vision and the way he wants the team to play, I am even more excited for the future. I still have major ambitions in the game, there is a huge amount that I know I can achieve, and this is the perfect place to continue my journey.”
United football director John Murtough added: “Christian has been one of the best attacking midfielders in Europe throughout his career. It is no surprise that he had so many options this summer, so we are really happy that he was convinced that this is the right club for him.
“In addition to his outstanding technique, Christian will add valuable experience and leadership skills to the squad, and we are looking forward to seeing the benefits of these qualities on the pitch this coming season and beyond.”
Eriksen counts Ajax Amsterdam and Tottenham Hotspurs among his former clubs.
