The 62-year-old was confirmed as United's new coach on Monday afternoon after signing a three-year deal at Old Trafford.
Mourinho, who worked under Van Gaal at Barcelona back in the 1990s, has wished his former colleague the best of luck ahead of his arrival in the Premier League.
When asked what he thought of the veteran Dutchman, the Portuguese told reporters: "A good man. He's a good football manager and I'm happy that he is joining me in the same country, but he's a good man. I wish him good."
Van Gaal will take charge of United when his role as Netherlands coach comes to an end following the World Cup.