The Argentina international officially signed for the Red Devils on Wednesday evening from Sporting Lisbon for around £16m.
The versatile Rojo can operate in a number of positions, and the Dutch boss highlighted what he feels the new man can bring to Old Trafford this term.
Van Gaal told United's official website: "Marcos is a very gifted defender. He has played at the highest level in world football and can play either as a central defender or left-back.
"He has ability, physical strength and a willingness to learn that means he has a very bright future ahead of him.
"He had a very strong World Cup and has been playing in Europe for a couple of years now. He is a very good addition to the team."
Meanwhile, as part of the deal, Nani has joined Sporting on a season-long loan.