United beat a host of their rivals - including Liverpool - to sign Depay from PSV Eindhoven.
PSV and United announced on Thursday that the 21-year-old forward would join the 20-time English champions in the summer, providing that he passes a medical, in a deal understood to be worth £25million.
Stam has watched Depay set the Dutch league alight with his performances this season and cannot wait to see his countryman turn out for his old club.
"He's a quality player," the former United defender told MUTV.
"United always want to attack and the club always has an interest in players that have a lot of pace and who can also play the one-vs-ones and create something or score goals
Memphis is that type of player.
"He's proven that in Holland for a couple of seasons now and also with the national team and I think it's a good step for him to join United now, and also work with (manager) Louis van Gaal because he knows him very well of course."
Depay's 21 goals helped PSV win the Eredivisie this season and now he is hoping for more success at his new club, who are fourth in the Barclays Premier League with three matches left.
''I always say; Dream, Believe, Achieve,'' tweeted Depay, who has the phrase tattooed on his torso.
''I was dreaming and believing of becoming the champions of the Eredivisie with PSV and we achieved it.
''I'm extremely grateful towards @PSV, all the fans, (sponsors) @UnderArmour and (agents)@SEG_Football for believing in me.
''Now it's time to set my goals again on winning trophies with @ManUtd.''
Depay will join fellow countrymen Robin van Persie, Daley Blind and manager Van Gaal at Old Trafford.
The player admitted it was tough deciding where to go next in his career, but is sure he made the right call in joining United.
''It was an exciting and pretty hectic period, and to have a choice between so many top clubs doesn't make it any easier,'' Depay said on his Facebook page.
''For me, Manchester United is an absolute dream club, so I didn't need any convincing (from) the guys who already play at Manchester United.
''They told me only positive things though, and I'm looking forward to playing with my Dutch team-mates next to all the other great players of Manchester United
And working with manager Louis van Gaal again is also a big bonus.''
Ronald Koeman, who was PSV manager during Depay's first year with the club's youth team, warned it will not be easy for the player to adapt straight away to the rigours of the Premier League.
"He has to develop himself and it will be tough for him because the Premier League is really tough in a physical way and a mental way," the Southampton manager said.
"You need very good quality to show, but for him it is a great challenge to be a player of Manchester United."
Source : PA
Source: PA