The Netherlands international, who was nominated for the PFA player of the year award, scored 26 top-flight goals as the striker played a big part in United’s title-winning campaign.
It was Van Persie’s first league title, and the 29-year-old hopes the Red Devils can push on and secure further success in the coming season under new boss David Moyes.
“It’s great but the road to the trophy is maybe even nicer,” Van Persie told United’s website.
“Being together every day and working on details, getting better step-by-step, beating opponents and then at the end of all that is the result and the trophy.”
He added: “It’s been an honour and I’m still thrilled about what’s happened in the last 10 months or so.
“Hopefully we can do even better, crack on and win even more trophies.”
Former Arsenal captain Van Persie completed a controversial £24m move to United from the Gunners in August 2012.