Despite details of the move emerging early in the day, United had to have an extension past the 11pm deadline to ensure the necessary documents were correctly filed with the Premier League.
They eventually announced Falcao's signing, which has an option to make the move permanent, at 1.30am, a deal which took United's summer spending past £150million
By that time, Arsenal had confirmed United striker Danny Welbeck had joined them, for a reported fee of £16million, after Falcao's arrival made his chances of regular first-team football even more remote.
And the presence of the Colombia international at the club's training complex late on Monday also spelled the end for Javier Hernandez, who earlier in the day joined Real Madrid on loan with a view to a permanent move.
United will pay Monaco between £5million and £6million for Falcao and will cover his wages, although they insist reports they will pay the 28-year-old almost £350,000 a week are wide of the mark.
The delay on confirming a deal which had been in the pipeline all day sparked rumours Falcao had failed a medical on the serious knee injury which kept him out of the World Cup but United insisted throughout that was not true.
"I am delighted Radamel has joined us on loan this season," said manager Louis van Gaal.
"He is one of the most prolific goalscorers in the game.
"His appearance-to-goal ratio speaks for itself and, when a player of this calibre becomes available, it is an opportunity not to be missed."
Van Gaal will hope he can kick-start a stuttering beginning to the season which has seen United take just two points from three Premier League matches, scoring only two goals, without even taking into account their embarrassing Capital One Cup exit to League One MK Dons
Van Gaal also needed reinforcements in defence after the loss of key personnel over the summer and they confirmed £14million Ajax defender Danny Blind had signed a four-year contract.
"Louis van Gaal is a tremendously talented coach, I have worked with him at Ajax and also for the Netherlands national team and I cannot wait to work with him at the biggest club in the world," the Holland international told manutd.com.
United's rebuilding has already seen them acquire midfielder Ander Herrera, defenders Luke Shaw and Marcos Rojo and British-record signing Angel di Maria.
Tom Cleverley looked to be moving to Aston Villa and then his preferred destination of Everton but the latter could not meet United's asking price.
However, United duo Nick Powell and Tom Lawrence both moved to Leicester on loan and permanent deals respectively while Michael Keane joined Burnley on a four-month temporary deal.
In his first interview as a United player, Falcao told MUTV it was a dream come true for him to play in the Premier League and predicted a "great" season for the new-look Red Devils.
The former Atletico Madrid hitman said of his move: "I t 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
"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."
He added of this new side: "We have very top players
I admire them
I want to meet them for the first time
I am sure that this season will be great for us."
Source : PA
Source: PA