Van Persie, last season's Premier League top scorer with 30 goals, completed his move from Arsenal on Friday after signing a four-year deal.
The 29-year-old had also been strongly linked with Premier League champions Manchester City after announcing in July that he would not his extend his contract, due to run out in 2013, with the Londoners.
"It wasn't an easy one," Ferguson told MUTV. "Understandably, [Arsenal manager] Arsene Wenger didn't want to sell to Manchester United. The boy wanted to come to us and that's important.
"He turned down various clubs to join us because he wants the challenge of coming to the biggest club in the world. I think that's fantastic.
"That's what swung it and what made it possible; the only negotiation left was agreeing a fee with Arsenal as there was no-one else in the picture because the boy wanted it and was desperate to come to Manchester United."
British media reported the deal to be £24 million, and Van Persie, who scored 132 goals in 278 appearances for Arsenal since joining from Feyenoord in 2004, is set to make his debut in United's Premier League opener against Everton on Monday.
Ferguson said the opportunity to sign a striker of Van Persie's calibre was too good to resist.
"I didn't think it was possible we could get Van Persie when we talked about it last year but, when I heard he'd refused to sign a new contract and made it publicly known that he wanted to leave Arsenal, then we had to be interested - there's no question about that," he said.
"Robin is a world-class striker with a proven record in England and in European football.
"His talents need no introduction to our fans - he has scored a number of goals against us in some classic battles with his former club. His movement, finishing and all-round ability are outstanding."
Despite his terrific season, Van Persie told Arsenal last month that he was unhappy with the direction they were taking.
Arsenal, who finished third in the Premier League last season, have not won a major trophy since the 2005 FA Cup.
"It's an honour to sign for Manchester United," Van Persie told the club's official website.
"I am looking forward to following in the footsteps of so many great strikers, bringing my experience and playing my part to help the team compete for the biggest trophies in the game. "I can't wait to get started."
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