The Colombia international's £6m loan move to Old Trafford dominated transfer deadline day as Louis van Gaal continued to splash United's cash - but Van Persie was bullish about the prospect of falling down the pecking order.
The Netherlands star, 31, said of the Monaco forward: "I welcome his arrival, he makes us better.
"At a top club you should always go for the best, which also fits my philosophy. Falcao must fight for his place, as I also have to. We must duke with Wayne Rooney and James Wilson to see who is playing."
Initial rumours had suggested 28-year-old Falcao was signed because impending knee surgery will sideline Van Persie for a significant portion of the season - but the former Arsenal star has quashed the claims.
Van Persie added: "I am impressed that people can pick up the imagination to invent something like that.
"I do not know where it comes from and can say with my hand on my heart that I won't be in a hospital to have the operation."