The Colombia striker will cost United between £5m and £6m and the club have confirmed they will pay his wages. However, the Red Devils insist reports they will pay the striker almost £350,000 a week are wide of the mark.
United have stuttered into the season under new manager Louis van Gaal, picking up just two points from three Premier League matches and crashing out of the Capital One Cup, losing 4-0 to League One MK Dons.
The Dutchman desperately needs something to kick-start their campaign and 28-year-old Falcao, who arrived in Manchester early this evening for his medical, could be it.
United's deal represents a remarkable turn of events on a day which began with reports that Manchester City and Arsenal were considering bidding for the player.
Falcao, who has only recently returned to fitness after the serious knee injury that ruled him out of the World Cup, was also heavily linked with Real Madrid last week.
However, their back line needs just as much attention, if not more, after the loss of key personnel this summer so the arrival of Ajax defender Daley Blind for £13.8, confirmed by the Dutch club just over three hours before the deadline, was another welcome addition.
United's rebuilding has already seen them acquire midfielder Ander Herrera, defenders Luke Shaw and Marcos Rojo and British-record signing Angel di Maria.
Heading out of Old Trafford, however, was Mexico forward Javier Hernandez as he joined Real Madrid on a season-long loan with the European champions having an option to buy at the end of the spell.
Hernandez, who joined United from Guadalajara in 2010, scored 59 goals in 154 appearances for the club but never became a regular starter.
Blind, 24, had long been expected to join his former Holland boss van Gaal at Old Trafford and the deal was finally signed off just over three hours before the end of the window.
Blind has agreed a four-year deal with United and his versatility will provide options for Van Gaal, whose initial attempts to shift United to 3-5-2 have proved a struggle.
Blind is comfortable across the back line, at wing-back or as a defensive midfielder.
He said: "It is a real honour to sign for Manchester United.
"I have been at Ajax since I was seven years old and I will always have very fond memories of the club and of my time there.
"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 United boss added: "I am delighted Daley has signed for the club.
"He is a very intelligent and versatile footballer that can play in many positions.
"Daley is a great reader of the game, he has played under my philosophy over a number of years and he will be a great addition to the team."