The 21-year-old will finalise a £31m move to Old Trafford when the transfer window opens in June.
Depay made his final appearance for PSV on Sunday, playing 83 minutes of their 3-2 victory at Den Haag.
He finished the season as Eredivisie's top scorer with 22 goals as PSV secured their first Dutch title since 2008.
PSV Eindhoven winger Memphis Depay has completed a medical at Manchester United.