The Colombia international has inked a four-year deal with the Ligue 2 champions and will be announced as the club's marquee signing shortly
The 27-year-old has long been the subject of intense speculation with club such as Real Madrid, Chelsea and Manchester City all keen to lure him away from the Vicente Calderon this summer.
However, he will continue his career at Monaco instead after signing a four-year deal with the Stade Louis II side on Tuesday.
Falcao already completed his medical earlier this week and all that is missing as of Wednesday morning is official confirmation from the ambitious Ligue 2 champions.
Sources close to the player have revealed that the parties involved in the deal had been in talks for several months, with Atletico agreeing to let go of their star striker once they had secured qualification for next year's Champions League.
The Colombia international becomes Monaco's fourth high-profile signing of the summer transfer window after the previous capture of Joao Moutinho and James Rodriguez from Porto for a combined fee of €70 million, and Ricardo Carvalho from Real Madrid on a Bosman move on Tuesday.