News broke via respected outlets De Telegraaf and Voetbal International, who both carried stories claiming that the Netherlands international would move to Old Trafford, with the former putting the fee at €30 million (£22.3m).
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PSV then announced on their Twitter feed that the club had agreed to sell the 21-year-old forward.
And PSV were quickly joined by United, who confirmed the news themselves.
Depay himself went on Twitter to give his thoughts around the first big transfer deal of the coming summer.
It is said that Depay, who is the top scorer in the Eredivisie with 21 goals this season, will sign a contract until 2018 as he links up again with the man who coached him at the World Cup last summer, Louis van Gaal.
The BBC and the Manchester Evening News said the likely transfer fee would be much higher than the figure stated in the Dutch press.
Depay recently travelled to England for talks with United and Liverpool and at one stage was said to be leaning towards a move to Anfield.
But now United have tied up the signing of Netherlands' most exciting young player.
After a shaky start to life as Manchester United chief executive, Ed Woodward is now really getting into the swing of things. Luke Shaw and Ander Herrera were both signed before the end of last season and the start of what is expected to be another big summer of spending has been signalled by the Depay news.
The 21-year-old is still a developing talent but already he has shown what quality he possesses and he will present no surprises to Van Gaal having played for him at the World Cup finals, and impressed too. Comparisons with Cristiano Ronaldo are premature, but we are certainly excited to see what Depay can do in English football.
Memphis Depay of PSV Eindhoven reacts during their Europa League soccer match against Zenit St Petersburg in Eindhoven February 19, 2015
Image credit: Reuters
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