It brings to an end one of the most intriguing transfer sagas so far, as the prolific Colombian was linked with a whole host of clubs including Real Madrid, Manchester United and Manchester City.
Dmitry Rybolovlev's latest acquisition will have sent shockwaves through the European game.
In a statement, he said: "We are proud to have secured one of the best players in the world and confident he will help Monaco regain its rightful status," said Rybolovlev.
"We are absolutely delighted that Radamel Falco has accepted the challenge of coming to play for AS Monaco."
Radamel Falcao sharing the news with his followers (RADAMEL FALCAO TWITTER)
Monaco have had to shelve their transfer plans for Radamel Falcao
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Falcao, who hit an incredible 35 goals in 46 league games during his time at Atletico Madrid, took to Twitter to share the news.
He tweeted: "I want to share with you that I will be player of @ASMFC_MONACO next season. I'm eager to start this challenge! I count on you support!"
Meanwhile, Monaco were dealt a setback as Victor Valdes pledged to see out the remaining year of his contract.
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