Man United announced the signing of Memphis on Friday after the player passed a medical last month.
The Dutchman, widely regarded to be one of the brightest young talents in world football, scored 22 league goals last term as he fired PSV Eindhoven to the Eredivisie title.
Van Gaal hailed Memphis but warned fans they must give him time to adapt to the Premier League.
Speaking about the signing, van Gaal said: “I know Memphis well from our time working together in the Netherlands national team. He is a young versatile player who has the ability to play in a number of different positions.
“It will take time for Memphis to get used to the rhythm of the Premier League but I have no doubt that he has the potential to become a great footballer for this club and he is at the right club to continue the good work he has done so far.”
Memphis clearly has a lot of confidence and the hope for United fans is that he has the talent to back it up.
The official announcement should be the start of an exciting summer in terms of incomings, with Roberto Firmino, Harry Kane and Rodrigo Dourado the latest names to be linked with moves to Old Trafford. Meanwhile, supporters will see Memphis playing in a United shirt for the first time during the club’s upcoming pre-season tour of the United States.