The midfielder has been capped 115 times for Denmark and scored 38 goals for his country. Eriksen has also played 237 games in the Premier League, registering 52 goals and 71 assists.
“Manchester United is a special club and I cannot wait to get started,” Eriksen said.
“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.”
Eriksen collapsed in the Euros tournament held last year and made comeback games last season with Brentford.
At United, he will play under new coach Erik ten Hag, a key factor in his decision to move to Old Trafford.
“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,” the player said.
“It is clear that he is a fantastic coach. Having spoken with him and learnt 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.”
John Murtough, Manchester United football director, said: “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.”