Eriksen becomes new manager Erik ten Hag, the second summer signing after the arrival of left-back Tyrell Malacia from PSV.
The 30-year-old attracted interest from many Premier League clubs, including former club Tottenham before interest cooled after his contract with Brentford expired.
The Bees were hoping to keep Eriksen beyond a short-term deal in January, but it was at Old Trafford that the Denmark international ended up.
Confirmation of the deal comes 13 months after Eriksen suffered in-game cardiac arrest, which saw the player, in his own words, ‘die for five minutes’ on the pitch at Euro 2020.
A remarkable return to top-flight football with Brentford followed seven months later and Eriksen was instrumental in the club’s fine late-season form.
Eriksen will now continue in the Premier League with United, three years after rejecting them while still at Spurs.