The Colombia international has repeatedly been linked with a move away from the Estadio Dragao, with top European clubs including Arsenal reportedly keen to acquire the highly-rated player.
AC Milan was also interested in signing Martinez but Atletico appears to have won the race to land the 28-year-old.
"We've completed the deal," Martinez's agent Luis Henrique Pompeo told Spanish sports newspaper AS.
"We want to thank AC Milan, who tried until the end, we feel very honoured but one cannot be in two places at the same time.
"Atletico is a very big club that has done important things domestically and in Europe and Jackson is going there with the will to achieve great aims and bring out the best of him.
"That's his hope. He is very happy and convinced he has made the right choice."
Atletico is set to pay FC Porto 35 million euro ($50 million) to acquire Martinez's sporting rights and the South American is expected to put pen to paper on a four-year deal.
Martinez joined Porto from Chiapas in 2012 and is under contract for another two seasons.
He scored 21 goals in 29 league appearances as his side finished runner-up to Benfica in the Primeira Liga this season.
Martinez is currently in Chile competing at the Copa America with his national team.
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