The Colombia striker admits Deadline Day was an unpleasant experience for him, as his loan move to Old Trafford almost fell through.
The 28-year-old was confirmed as a Man United player a couple of hours past the official transfer deadline but everything was finalised in time as he made the switch from Monaco on a temporary basis.
The deal is also believed to include an option to buy the Colombian permanently and Falcao says he is delighted to have made the move to Old Trafford.
However, he has revealed that the move did not come out with its stresses.
"No one has the idea of the stress I experienced at the time," Falcao is quoted as saying by the Daily Mirror. "The transfer almost wasn't achieved but thank God we had an additional hour and then it occurred.
"The first impressions that I took made a great impact on me. Manchester United is a great institution that lacks nothing and I'm happy to have taken this step.
"I'm very happy and excited to return to the team. The hard times [Falcao was out with a long-term injury last season] have made me grow as a human being and today
“I appreciate very much my life in football. I am very confident, I have scored goals again [for Monaco], and now I just want to play."
Manchester United's next Premier League game sees them host Queens Park Rangers after the international break.