Liverpool, Tottenham Hotspur, Bayern Munich and Paris Saint-Germain were all said to be interested in the 21-year-old but he eventually chose to join Man United on Thursday.
The signing has been widely praised by fans as Depay is considered to be one of the brightest young talents in Europe.
Scholes insisted Depay can be a success at United if he successfully adapts to life in the Premier League.
Speaking about the move, Depay said: ”He has scored 21 goals for PSV Eindhoven this season and is the Dutch league’s top goalscorer, which is a good sign.
“If he can have anything like the kind of impact Ruud van Nistelrooy made, he will be a great success.
“For some Dutch players, coming to England can be a difficult transition but this lad clearly has promise.
“It was encouraging from Manchester United’s point of view that they have made the signing of Memphis Depay at such an early stage. He has pace, which has always been a feature of great United teams, and has been badly lacking this season at times.”
Depay is already a sensational player and he will only get better under the guidance of Louis van Gaal.
The pair enjoy a good relationship on and off the pitch and van Gaal will know exactly how to get the best out of his compatriot in the coming years. However, fans must be wary not to expect too much too soon from the 21-year-old.