The Colombia international, who has scored 28 goals in 34 Liga appearances for Atletico Madrid this season, will join countryman James Rodriguez at the mega-rich Ligue 1 club
The 27-year-old was highly sought-after by Premier League clubs Manchester City and Chelsea, before a spectacular offer from the Ligue 1 outfit prompted a dramatic U-turn - as revealed exclusively by Goal.
Falcao, who has scored 34 goals in all competitions this season, joins former Porto team-mates James Rodriguez and Joao Moutinho in signing for the mega-rich French outfit.
"We are absolutely delighted that Radamel Falco has accepted the challenge of coming to play for AS Monaco," read a statement from the club's president Dmity Rybolovlev.
"We are proud to have secured one of the best players in the world and confident that he will help ASMFC regain its rightful status."
Falcao joins Monaco after just two years in the Spanish capital with Atleti, and is delighted to have joined Claudio Ranieri's big-spending side.
"I am very happy to join Monaco and very happy to wear these new colours," he said in a video message to fans.