Falcao's prolific strike-rate, which has been better than a goal every two games with Porto, Atletico and Monaco, made him one of the world's most sought-after forwards prior to his surprise move to the French club from Spain in the summer of 2013.
With Monaco aiming to cut costs and raise funds following the lavish spending of Russian owner Dmitry Rybolovlev, Falcao was allowed to follow fellow Colombian James Rodriguez out of the club.
The cruciate ligament injury sustained by Falcao in January, however, forced the player to miss the World Cup and raised doubts over his fitness - concerns which coincided with suggestions, which have been denied by United, that he is actually older than 28.
But despite not yet completing a full 90 minutes since returning from his injury during pre-season, Falcao has managed three goals in six appearances totalling 217 minutes for club and country and he insists he is fit and ready to play for United.
"Yes, I feel well," Falcao said. "I started to play two months ago with Monaco and I have improved a lot in the last months. I have scored goals and that is important to strikers.
"I am confident with my physical condition and I am comfortable with my knee. I feel very good in myself and I am happy to be here.
"So I don't think I will need too much time because United has very good players and that reason makes it easier to play football."
Manager Louis van Gaal, who defended his decision to sell Welbeck to Arsenal with a blunt appraisal of the forward's lack of progress at Old Trafford, claimed Falcao's performance in his first United training session offered instant justification of his decision to sign a player nicknamed "El Tigre".
"Today in training, he got one ball and it was in the goal," Van Gaal said. "He confirmed it [quality] in his first training session with me. But when I say this, I put too much pressure on him because I know it is very difficult to come from another club to Manchester United in a new process."
Van Gaal dismissed fears over striker Robin van Persie's fitness and suggestions of impending knee surgery. "Van Persie is fitter than before the World Cup," he said. "Maybe you remember I let him train the first three weeks before I let him play a game. He is more fit than ever before."