Van Gaal has signed a three-year contract to take over at Old Trafford after the World Cup, with Ryan Giggs as his assistant.
Mourinho said: "He is a great football manager and I am happy he joins me in the same country and the Premier League.
"But more important than that, he's a great guy, a great man and I wish him good."
Former United assistant manager Mike Phelan said Van Gaal's "strong personality" would make him the ideal fit to step into the considerable shoes of Sir Alex Ferguson.
Phelan worked with Ferguson for three years before departing alongside the Scot last summer.
Phelan told BBC Five Live: "I've met [Van Gaal] a couple of times and he's got a very strong personality about him.
"But at a club like Manchester United, that's what is required
You have to hit the ground running and I'm sure he will do.
"There's been a lot of talk about Van Gaal and his methods but he does the job a manager has to do and he's a very good coach."
Phelan said he expected Van Gaal not to be overawed by the prospect of taking over such a big club and would set to work immediately to improve the squad after a disappointing campaign under David Moyes.
Phelan added: "He's not stepped into the shoes of Sir Alex and all the history that comes with Sir Alex, and he's now going to have to get the players to perform better than they have done in the past season.
"There's a lot of talk about new players coming into the club and I'm sure when the new manager comes in he'll have his favourites.
"Man United have said they have money to spend so I'm sure as a manager he'll spend it
I think this time because of the disappointing season they had last year there is room for changes."
Source : PA
Source: PA