The former Netherlands striker moved to the Red Devils in 2001 and scored 150 goals in 219 appearances over five years at the club.
Van Nistelrooy was speaking at an event to unveil a statue of the 70-year-old at Old Trafford and hailed the manager's ability to get the very best out of his squad, as players and people.
"It's great to be back," the Dutchman told reporters. "Especially as it is to pay respect to the manager, who deserves all the credit for today. He's the reason we are here.
"I had a great five years [at Manchester United] and I want to pay my respects. I'm very grateful for the chances Sir Alex gave me.
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"He's able to get the best out of people. He did that with me as well. Not just on the pitch but off it he gave me a lot, which I am very grateful for.
"Of course, we had our things with the way it ended at the club. But overall I look back on a great time here with a lot of respect for him."
The Dutchman left United in acrimonious circumstances, falling out with Sir Alex over a lack of first-team involvement before heading to Real Madrid in 2006, but insisted that he did not bear a grudge towards his former manager for showing him the door.
He added: "When he is building new teams he is willing to do that [be ruthless]. That is all credit to him. The club is the most important thing.
"That is what he always said. It is his most-repeated sentence. He proves that. You move on. I moved on to Madrid and had four great years there. He moved the club further onwards. It is fair enough.
"I didn't find it hard to deal with. I accepted it. I am grateful for five great years here and it gave me another opportunity to be part of Real Madrid for a good while and be successful there. It opened up a door and I moved on. Thank God, that was a successful period as well."Van Nistelrooy hailed the 70-year-old's longevity at the club, describing the Scot's Old Trafford reign as "out of this world."
"It is incredible," he said. "It is difficult to get your head around. Twenty-six seasons!
"Ten years in football is an awful long time for a manager to be at a club. He is going on and on. In three or four years we will be talking about 30 years. It is out of this world.
"But he's doing it. As he said, he has outlived death. He is outliving everyone."