Eriksen became a free agent last month after his six months deal at Brentford expired, but will now sign a three-year deal at Old Trafford.
However, the 30-year-old midfielder must first go through significant medical tests at Old Trafford before the deal is completed.
Having suffered a cardiac arrest on the pitch at Euro 2020 last summer, Eriksen was released by Inter Milan as the Serie A side could not keep him because of league laws.
But he signed for Brentford in January, scoring one and assisted four in 11 games during his spell at the London club.
Brentford held ‘positive talks’ with him at the end of last month and were hopeful about luring the playmaker back to west London. But the player has chosen to go to Manchester where he is set to become the club’s first signing under ten Hag.
It is hoped that the signing of Eriksen will please Cristiano Ronaldo, who has asked to leave the club after growing frustrated with their transfer activities.
The Portuguese wants the Old Trafford club to show commitment and clarity in their transfer business, which has seen them linked to many players but still unable to get one deal over the line.