The Dutchman, who believes the boss must be feeling some relief at making the decision, obviously refused to be drawn on any successor - jokingly nominating Fred the Red as his choice!
Meulensteen was asked by Sky Sports News when he found out about the big story and replied: "Just this morning when I came to the club. He called us into his office and said what decision he has taken.
"It's always been on the cards - there has been speculation every season but the manager kept his cards close to his chest. He felt the time is right now and he's made that decision.
"He's obviously a man that thinks very, very hard and I'm sure he's taken a lot of thought in making this decision. I wish him all the best - he's been fantastic for the club, for Manchester United, and I'm hoping the fans give whoever comes in the same support as he gets."
The manager, predictably, ends on a high after guiding the team to a 13th Barclays Premier League title, the 20th overall, with the celebrations set to go into overdrive at Old Trafford on Sunday when the trophy will be lifted.
"I think we've responded really well to the big disappointment we had last year," added Meulensteen. "There was a determination around the whole place, especially from the manager, and he's delighted we won the title in the way we did."