"#mufc is delighted to announce Radamel Falcao has joined on a 1-year loan from Monaco with an option to buy," the Premier League team said on its Twitter feed.
Falcao was in Manchester for a medical examination ahead of the proposed season-long loan from Monaco, a move revealed to Reuters on Monday by a source close to the deal.
The 28-year-old scored 11 goals in 20 appearances for Monaco after joining from Atletico Madrid for a fee of around 50 million euros last year.
"I am delighted to be joining Manchester United on loan this season," Falcao said on United's website (www.manutd.com).
"Manchester United is the biggest club in the world and is clearly determined to get back to the top. I am looking forward to working with Louis van Gaal and contributing to the team’s success at this very exciting period in the club’s history."
Falcao, who missed the World Cup after suffering a serious knee injury, had been linked with several top European clubs, including Real Madrid.
He will compete with regular strikers captain Wayne Rooney and Dutchman Robin van Persie for a place in a reshaped United team.
"I am delighted Radamel has joined us on loan this season," Van Gaal said.
"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."
Financial details were not disclosed but British media reports suggested the deal cost United 6.0 million pounds (9.96 million US dollar).
Manchester United earlier completed the signing of versatile Netherlands international Daley Blind and the Falcao move tipped the club's summer spending spree past 150 million pounds following the British record transfer fee paid to Angel di Maria.
They will recoup some of that cash after selling England forward Danny Welbeck to Arsenal, while Mexico striker Javier Hernandez has also departed on a season-long loan to Real Madrid.
United are still looking for their first win under Van Gaal having drawn two and lost one match in the Premier League and crashed out of the League Cup 4-0 to lower league MK Dons.
(Reporting by Ian Ransom in Melbourne, editing by Nick Mulvenney; Editing by Nick Mulvenney)
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