"It’s done, I can confirm that everything’s ready,” Martinez told reporters after Colombia lost on penalties to Argentina in the Copa America quarter-finals on Friday.
“For now I’ll go and enjoy time with my family, then I’ll travel to Spain to join my new club,” the 28-year-old said.
“I’m really excited about this move to Atletico Madrid, I take it as a new challenge in my career and hope things work out well for me there.”
Coach Diego Simeone’s Atletico side were short of a striker after Croatian Mario Mandzukic moved to Juventus.
"I’ve evolved a lot as a forward,” Martinez said. “I’m still growing and learning and will surely be able to improve a lot of things in my game in a league like Spain’s.”
Martinez had signed a contract with Porto until the end of the 2016-17 season but Spanish sports daily As reported this week that Atletico had agreed to pay his buyout clause worth 35 million euros (25 million pounds).
Martinez graduated from the Independiente Medellin youth academy to the first team before joining Mexico's Chiapas in January 2010 and moving to Porto in 2012.
A versatile player who is adept at shooting with either foot and is strong in the air, he has been the leading scorer in Portugal's top flight in each of his three seasons, netting 26 goals in 2012-13, 20 in 2013-14 and 21 in 2014-15.
(Reporting by Camila Ramirez, additional reporting by Iain Rogers in Madrid; Writing by Rex Gowar, editing by Ed osmond)
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