"It was sealed today," the agent, Luiz Henrique Pompeo, told the newspaper, adding that AC Milan were also chasing the 28-year-old forward.
"It (Atletico) is a very big club which has had a lot of success in its league and in Europe and Jackson is going there full of desire to do great things," Pompeo added.
Martinez signed a contract with Porto until the end of the 2016-17 season and AS said Atletico had agreed to pay his buyout clause worth 35 million euros.
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The La Liga side are also poised to complete the signing of Villarreal's Argentine forward Luciano Vietto, Villarreal president Fernando Roig was quoted as saying on Monday.
Martinez graduated from the Independiente Medellin youth academy to the first team before joining Mexico's Chiapas Jaguares in January 2010 and then moving to Porto in 2012.
A versatile player who is adept at shooting with either foot and is also strong in the air, he has been the leading scorer in Portugal's top flight in each of his three seasons, scoring 26 goals in 2012-13, 20 in 2013-14 and 21 in 2014-15.
He is playing for Colombia at the Copa America and was a second-half substitute in their defeat by Venezuela and draw with Peru. They face Argentina in the quarter-finals on Friday.
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