The 25-year-old striker has been a prolific scorer for Porto since joining from River Plate in 2009 and last season helped the club win the Portuguese league and cup double as well as the UEFA Europa League. His signing will help cover the loss of Argentina ace Sergio Aguero, who left Atletico for Manchester City this summer.
A statement on the Atletico website read: "Atletico Madrid and Porto have reached an agreement for the transfer of Radamel Falcao to the Rojiblancos. The Colombian striker, top scorer in last season's Europa League with 17 goals, will sign a contract for five years with our club."
An announcement from Porto to the Portuguese Securities Market Commission (CMVM) revealed the fee to be €40 million, although the provision for "variable compensation" could see that total rise to €47 million.
Falcao will now travel to Madrid to discuss personal terms and undergo a medical.