According to reports by sports dailies El Mundo Deportivo and Diario As, Radamel Falcao has signed a five-year deal with the French second division champions.
It is said Monaco will pay the Colombian sharpshooter a staggering €14 million in annual tax free earnings.
Radamel Falcao passed his medical on Tuesday and then, together with his agent Mendes, met Monaco's president Dmitry Rybolovlev.
Barcelona goalkeeper Victor Valdés is also said to be be finalizing his transfer to the Principality club, according to various sources on Wednesday.
The French second division champions, backed by Russian billionaire Dmitry Rybolovlev, are looking to make a splash when they rejoin the top flight next season after a two-year hiatus.
Falcao, 27, who has banged in 28 goals this season and won the Spanish Cup a year after helping Atletico de Madrid to a Europa League triumph, has now become the most expensive player in French football history.
He only joined Atleti two years ago in a €40 million deal after firing Porto to Europa League glory.
Valdes, 31, is out of contract with Barcelona at the end of the season and had already revealed back in January he would be leaving the Catalan giants.
Valdes has spent 10 years at Barca and won the Champions League three times and Spanish La Liga six times during that period, as well as two King's Cups.
The double capture would take Monaco's post-season spending spree to well over the 100 million euro mark following the arrivals of Portugal midfielder Moutinho and Colombian winger James Rodriguez from Porto for a combined 70 million euros.
Apart from building the most expensive team in French football history, Rybolovlev's money could help Monaco rival the other Ligue 1 big spenders Paris Saint-Germain, who are backed by Qatari money.