The Colombia international is joining United for a loan fee of £6m and will be paid a reported £346,000 per week during his season at Old Trafford.
United are also believed to have the option to complete the permanent signing of the Monaco star for £52m.
The deal had not been completed by the 11pm deadline and Manchester United required an extension in an effort to get the deal done in time.
“It’s a dream come true to join a club like Manchester United, one of the biggest clubs in the world,” Falcao told the Independent.
"I’ve always dreamt about playing for one of the truly great teams and winning lots of trophies.
"It is a once in a lifetime opportunity and you can’t turn that down. I’m a huge fan of English football and watch it whenever I can. Now the reality is I’m going to play there.”
- Sports & Recreation
- Manchester United