The 28-year-old has scored 11 goals in 20 appearances for Monaco after joining from Atletico Madrid for a fee of around 50 million euros ($65.70 million) last year.
Colombia international Falcao, who missed the World Cup after suffering a serious knee injury, had been linked with several top European clubs including Real Madrid.
Falcao will compete with regular striker Wayne Rooney and Robin van Persie for a place in Louis van Gaal’s new-look United side. (Reuters)
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