The Colombia international is expected to fly to Manchester to undergo a medical ahead of a sensational transfer deadline switch from Monaco to Old Trafford.
The Colombia international, who recently recovered from the cruciate knee ligament injury that ruled him out of most of last season and the World Cup, had been the subject of interest from Arsenal and Manchester City. But United is understood to have won the race to sign the 28-year-old.
Falcao will fly in to Manchester today on a private jet from Nice to undergo a medical and complete the formalities of a switch from Monaco.
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Goal understands that United will pay a 10 million-pound-plus loan fee for the 28-year-old in addition to a significant portion of his £300,000-a-week Monaco wages.
The deal was believed to have been agreed in the early hours of transfer deadline day as the Premier League giant clinched the latest in a series of big-money deals this summer. The capture of Falcao follows the arrivals of Angel di Maria, Luke Shaw, Ander Herrera, Marcos Rojo and Danny Blind.
The Colombian star will replace Javier Hernandez in the United squad, with the Mexican signing for Real Madrid on a season-long loan on Sunday night.
United's move will be regarded as another huge statement of intent as Louis van Gaal continues the transformation of his squad following a disastrous start to the new season for his team.
City had appeared to be in pole position to capture Falcao after his proposed move to Real collapsed at the end of last week.
A deal had been close, with Falcao appearing to have been identified as the player to replace Alvaro Negredo in Manuel Pellegrini's squad. The Spaniard has agreed to terms on a season-long loan to Valencia.
It is also a blow to Arsenal, after Arsene Wenger had sanctioned a pursuit of Falcao on the same terms as the season-long loan he has agreed with United.
Wenger, who also lost out on Loic Remy over the weekend, will now have to consider a fallback option as be searches for a replacement for long-term absentee Olivier Giroud.