The 29-year-old has scored 22 goals this season in just 30 appearances for the Red Devils in all competitions.
Van Persie told reporters: "It's gone as well as I've expected it to go. I go into work every day whistling — as from the first day they've made me feel welcome.
"The boys made me feel right at home. Training is really good and I see things I've not seen in a long time.
"It is a very pleasant environment to work in. Every day I work on new things. I have become alert to small details that make me better."