The AS Monaco striker's loan agreement was confirmed by United almost two hours after the summer market shut.
"Yes, it was a very long day. 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," Falcao told MUTV.
"I am very excited for that. 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.
"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."
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