Falcao joined United on a season-long loan from Monaco after Monday's transfer deadline closed, with special permission given to the Old Trafford outfit to complete the deal.
The 28-year-old forward can be bought by United at the conclusion of his loan spell and that is a move the player would clearly embrace.
A delighted Falcao told MUTV: "For me, it was a dream to play in the Premier League.
"I always wanted to be here because this league is very good, it has very good teams and Manchester United is the best team in England. Everything is perfect for me.
"I am very happy to be part of this big club. I've waited for this moment during a lot of the year."
Falcao admitted that he was nervous his move to United would not go through, with a delayed flight that took him to Manchester only adding to the drama.
But with the move now sorted, Falcao – who scored 13 goals in 22 appearances for Monaco – is keen to link up with manager Louis van Gaal and his new team-mates.
"It was a very long day," he added.
"It was hard, difficult. We were waiting until the last minute but I didn't lose my faith. Now I want to say thank you to God for this. I'm very happy.
"I am very excited for that [to work with Van Gaal]. Van Gaal is a very good trainer with a lot of experience. I want to do the best for the team, for him and for the supporters."
Falcao's arrival capped a big transfer window for United, who also signed Angel di Maria, Ander Herrera, Luke Shaw, Marcos Rojo and Daley Blind.
It took their reported spending to approximately £150 million as they seek to recover from a terrible start to the season.
Van Gaal's men have taken just two points from three league matches, while MK Dons stunned them 4-0 in the second round of the League Cup, but Falcao is confident they can respond.
"We have very top players," he continued.
"I admire them. I want to meet them for the first time. I am sure that this season will be great for us."
