The former Tottenham manager feels the Netherlands international could build a mouth-watering partnership with Wayne Rooney and guide the club to another league championship.
It was announced by both clubs on Wednesday that a fee, thought to be in the region of 24 million pounds, had been agreed for the sale of the 29-year-old with the forward due to travel to Manchester on Thursday to complete a medical and put pen to paper on a four-year deal.
The former Tottenham manager has predicted that the goals Van Persie is capable of bringing to Sir Alex Ferguson's side could see the Red Devils reclaim the title from their local rival.
"I could see Manchester United winning the league next year, now they've got Van Persie," Redknapp told BBC Sport. "He could be the difference. He really is a great signing."
Van Persie and Wayne Rooney - first and second respectively in last season's goalscorer rankings - notched 57 goals between them in the Premier League during 2011-12, which is more than 15 of the division's clubs achieved in total.
Redknapp believes the prospect of the pair linking-up is mouth-watering.
"If he performs like he did last year then him and Rooney will just be an incredible partnership," he remarked.
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