Eriksen, who needed life-saving treatment on the pitch last year when he suffered a near-fatal cardiac arrest in a European Championship match against Finland in June, returned to action with Brentford after signing a short-term deal in January.
Eriksen is United's second recruit in the close season under new Dutch manager Erik ten Hag (52) after the club signed Dutch left back Tyrell Malacia (22).
"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," Eriksen said in a statement.
"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."
Eriksen was an Inter Milan player when he collapsed and underwent surgery to be fitted with an Implantable Cardioverter Defibrillator (ICD) device -- which is not permitted in the Italian Serie A -- leading to the termination of his contract.
After signing for Brentford, he made 11 league appearances under Danish coach Thomas Frank, scoring a goal and providing four assists as Brentford finished 13th in their first season in the Premier League.
He is no stranger to the Premier League, however, having spent nearly seven seasons with Tottenham Hotspur, making more than 300 appearances in all competitions for the London side.
He also resumed his Denmark career, scoring against Serbia on his return to the Parken Stadium where he had collapsed.
"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," Eriksen added.
United, who finished sixth last season and failed to qualify for the Champions League, kick off the new Premier League season with a home game against Brighton & Hove Albion on Aug. 7.
