Rooney had become disillusioned with life at Old Trafford before Moyes succeeded Sir Alex Ferguson.
But, within months, he had committed himself to a new long-term contract that will keep him at United for life.
Moyes told the Sunday Mirror: "When I arrived at United, it was well known that Wayne wasn't in a good place.
"He was a bit down and I told him I needed to see the old Wayne Rooney.
"I asked him to get back to being that hungry, aggressive player, who I'd seen at Everton.
"Sometimes, he does overstep the mark, but I always thought that it is better to have Wayne Rooney straining at the leash rather than playing within himself.
"His response was to get himself in his best physical condition and he was terrific for me at United."
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