The Dutch striker joined United from Arsenal this summer but Ferguson has revealed that he had doubts about the deal.
"I never thought we would get him, until he convinced us that he wouldn't be signing a new contract at Arsenal," said Ferguson. "We just started working hard with Arsene Wenger and myself, I phoned him quite a few times, and we eventually came to an agreement.
"If Robin had more than one year left on his contract, we would never have got him.
"It was very amicable with Arsene. He made his case because, first of all, he wanted him to stay without contradiction. There's no doubt about that and he worked hard to keep him. The next stage, once he accepted that he had to let him go, was to make sure we paid him the money. And Arsene has always done a phenomenal job getting top dollar for players."
Arsenal travel to Old Trafford to face United on Saturday.