The Colombian striker has moved to Old Trafford on an initial one-season loan from AS Monaco and is excited about beginning 'a big challenge in his career'.
"I'm very happy to be here, it's a big challenge for me, for my career and I always dream to be in a club like Manchester United," he told reporters at his official unveiling.
Falcao also suggested that he would like to be part of United's project on a more long-term basis.
"It is a new process, a new team. This year some players have come in and I think Manchester United are building a big team for this season and future seasons I would like to be here and be part of this project."
The 28-year-old could make his Red Devils debut when they face Queens Park Rangers on Sunday.