Van Gaal has agreed a three-year deal at Old Trafford and will take charge of his first English club as soon as Holland's World Cup campaign is over, with the United striker set to captain the national side in Brazil.
The pair have worked together for the past two years on the international stage and enjoy a good relationship as van Gaal handed the 30-year-old the armband on a permanent basis last summer, while reports have suggested that he may be set to do the same at United following Nemanja Vidic's departure.
Van Persie had been linked with an exit from Old Trafford, but says that van Gaal is somebody who can help to get the best out of him after a stop-start season due to injuries.
"I have enjoyed the past two years with Holland a great deal," he is quoted in The Sun Sunday.
"He is very clear in what he says. I am now going to go through another two-year process with Van Gaal and I am looking forward to it.
"It is a different sort of approach to what I was used to with previous coaches, but I like it.
"It is a very Dutch way of doing things - very direct but intended to make us better players."
United team-mate Danny Welbeck, currently part of the England squad as they prepare for the World Cup, has also spoken of his delight at van Gaal being named the new boss.
Welbeck said: "I am happy. He is a great man, a great manager. Looking at his CV tells you he has managed at some big clubs."