De Boer worked closely as a player under Van Gaal at club level with both Ajax and Barcelona as well as with the Netherlands.
Van Gaal's Old Trafford tenure will officially get under way when the 62-year-old's time as Netherlands coach finishes after the FIFA World Cup.
And De Boer is in no doubt that the veteran coach will immediately lift spirits at United following David Moyes' ill-fated spell in charge.
He told MUTV: "I think you are getting one of the best managers in the world so the chance of success is high.
"I believe that, especially when you have patience, he will get success because he's so determined to do well but also he has a great vision.
"On his tactics, he will know the weak points of the opponents, and what the team needs, so he can really make a very strong team and a team that believes in each other.
"Sometimes it takes time to get that belief from the players, some will not accept that and will drop off, but when you have everybody together, believe me, you will have great success.
"I've seen so many coaches and he stands out so far ahead."