Mourinho hails Van Gaal appointment
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."
Veteran United defender Rio Ferdinand, who recently confirmed he will be ending his 12-year association with the club, tweeted: "Good luck to Louis Van Gaal as the new manager of @ManUtd also to Giggsy as no.2. Hope they get #mufc back to the top where we belong."
Meanwhile, former United and Liverpool striker Michael Owen warned the club's current stars they would have their work cut out if they wished to impress their new boss.
Owen tweeted: "If reports are true, Van Gaal's appointment will be a culture shock to the current squad. Good to see Giggs kept on. Board directive?"
Former United keeper and Van Gaal's compatriot Raimond van der Gouw told BBC Radio Five Live: "Yes, I think he's absolutely the right man.
"He's a very good and experienced manager for Manchester United.
"David Moyes doesn't have the same experience. He was not very lucky this season."