The former Atletico Madrid and Porto striker arrived in a deadline day loan move from Monaco, with a view to a permanent switch.
Despite his new club's poor start to the 2014/15 season, and the fact he is only just returning to fitness following the seven-month injury layoff which saw him miss the World Cup, the 28-year-old is confident he can fire the Red Devils back to the top of a league he considers the world's best.
"[My target is] to score goals and win titles," he told FourFourTwo. "The aim this season is to win the title. It is important for me to help my club and Colombia as we prepare for the Copa America and the next World Cup for 2018.
"The Premier League is the best league in the world. The best players are there and you get to challenge yourself each week against the best.
"That is important for a player, like myself, who is looking to improve, score more goals and win trophies. This is a great opportunity for me."
Falcao had long been touted to leave Monaco, who he joined from Atletico Madrid last summer, but his destination was expected to be either Real Madrid or Manchester City, not United.
The prolific striker insists that, although there was interest from the Spanish capital, a move to the 20-time English champions was always his preference - even if the last-minute nature of the move caused him some strife.
"Manchester United had been pursuing me for the past few months," he explained. "Yes, other clubs like Real Madrid were interested, but I wanted to go to Manchester. It is a great club, with a great history and one that fills me with a lot of hope that I can succeed there.
"There were moments where I didn't think the transfer would occur in time - something that was stressful to me - but in the end it worked out. Like I said, this is a great opportunity for me, especially after my injury."
Falcao will team up with new United boss Louis van Gaal. The Dutchman is yet to win a competitive match since taking over in July - suffering a humbling 4-0 defeat at MK Dons in the League Cup - but Falcao is confident the 63-year-old former Ajax and Barcelona coach is the man to lead the Red Devils to glory.
"We all saw at the World Cup that Van Gaal is one of the best managers in the world," said the Colombian. "I think he is the type of person who understands his players and gets the most out of them - that is important in order for a player, and also for a team in general to succeed."
Falcao could make his United debut against Queens Park Rangers on Sunday.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.