United, who have managed only two points in three league games under new coach Louis van Gaal so far this season, paraded Falcao and fellow new signing Daley Blind to the press and cameras before their expected debuts against Queen's Park Rangers this weekend.
The club signed the Colombian striker, who has spent most of the year out injured, on loan from Monaco just before the transfer market closed last week, in a deal that some commentators said smacked of desperation.
But Falcao, 28, speaking in careful English, said all the right things.
"I feel good. I have had a great welcome. Any settling in period is easy when the quality of players is so good," the Colombian, who joins Robin van Persie and Wayne Rooney in United's attacking line-up, said.
Falcao's anterior cruciate ligament injury kept him out of the World Cup. He played some pre-season friendlies with Monaco and some 15 minutes of Colombia's defeat by Brazil last Friday.
"I feel well," said Falcao, who scored seven goals in his first seven games for Monaco last season. "I started to play two months ago with Monaco. I've improved in the last month. I've scored goals which is important to a striker."
"I'm confident with my physical form and I'm comfortable with my knee."
Van Gaal, appointed after United finished in an unaccustomed seventh last season under David Moyes, has been criticised for splashing out 150 million pounds on new players.
Former United defender Gary Neville said in a radio interview: "Falcao tipped them over the edge, it surprised and shocked everyone. How (van Gaal) gets them (all) in that team I don't know."
"It's not the way I would expect United to go about their  business. I thought it would be more controlled," Neville, now an England assistant coach and television commentator, said.
Van Gaal also broke the English transfer record in buying Argentine Angel Di Maria from Real Madrid.

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