The Colombia striker made his first international appearance since Janaury against Brazil on Saturday with a brief 13-minute run-out in Miami.
Falcao scored twice in three Ligue 1 appearances before leaving Monaco for Old Trafford on a season-long loan, showing few ill-effects of his torn anterior cruciate ligament sustained against part-timers Chasselay in last season's Coupe de France.
The injury forced Falcao to miss the World Cup and he concedes doubts will remain with him until he can prove his fitness to Louis van Gaal, despite feeling "spectacular", with a debut likely to come against QPR next weekend.
"Because of the injury I felt so nervous," Falcao is quoted by British media. "Almost like it was my first time with the national team.
"And I expect it will be the same before I play my first game for Manchester United.
"I'm so happy to be back, and I am also happy about being able to join United.
"Physically I feel spectacular. I have been able to play without any kind of trouble.
"I am very excited about playing for Manchester United, and I hope to score a lot of goals for them. That is something I have done everywhere I have played.
"It is a dream come true to play for such a great and famous club. To bring the good times back is what we all want, and I will work extra hard to do that. I made the right choice to join Manchestrer United.
"United was always in my best interests. I have been trying for months to get it all sorted out and I was so happy that United came to an agreement with Monaco.
"United are one of the three best clubs in the world. They have made me feel very important in this project."
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