It was announced by both clubs on Wednesday that a fee, thought to be in the region of £24 million, 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.
And 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 rivals.
"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.
|AT THE DOUBLE?
|13/2||Robin van Persie is 13/2 to score two or more goals for Manchester United versus Everton with Paddy Power|
And Redknapp believes the prospect of the pair linking-up together is mouth-watering.
"If he performs like he did last year then him and Rooney will just be an incredible partnership," he remarked.
The striker's future has been the main talking point of much of the summer and former England manager Graham Taylor has praised Sir Alex Ferguson for tying up a deal for Van Persie in light of interest from elsewhere, namely local rivals Manchester City.
"Ferguson's done it again," Taylor proclaimed. "This gives United an edge in the title race. If Robin van Persie performs like he has done for Arsenal he's going to be a great addition."