The Danish midfielder had Spurs, Brentford and United all interested in his services but has now chosen the Red Devils, where he will work under new boss Erik ten Hag.
According to David Ornstein from The Athletic, Eriksen has told United he wants to play for them and is willing to sign the three-year deal they have put on the table.
The transfer will go through upon the completion of final contract details and a successful medical.
He is line to become United's second addition of the summer, following on from the capture of Feyenoord left-back Tyrell Malacia.
Eriksen had signed a short-term deal with Brentford in January and impressed in his 11 appearances for the Bees.
His chances of playing again were deemed to be slim following on from his cardiac arrest at Euro 2020 against Finland.
Eriksen made a swift recovery but because he had to be fitted with a ICD (implantable cardioverter-defibrillator), Eriksen was not allowed to play in Serie A due to their regulations on heart devices.
That meant he had his Inter Milan contract terminated in December when he realised it was possible to continue playing and began training for a return.
Brentford offered the former Spurs playmaker the chance to do just that and he put pen to paper on a six-month deal.
He made his first appearance against Newcastle, receiving applause from both sets of fans and players after entering the fray as a substitute.
Eriksen has also returned to the Denmark fold and made a fairytale comeback by scoring with his first touch against Netherlands at the Johan Cruyff Arena.
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