"Raul Jimenez is a new Atleti player. Open your wings and fly very high," America said on their official Twitter account (@CF_America).
Media reports claim the transfer fee for the forward's six-year deal was valued at more than 10 million euros ($13.4 million), a Mexican record.
"A successful conclusion has been reached to the most important and impacting sale in the history of Mexican football carried out by the America administration," the club said on their website (www.clubamerica.com.mx).
They added that Jimenez, an Olympic gold medal winner with Mexico at the 2012 London Games, had left for Madrid on Wednesday.
Atletico said the 23-year-old striker, who scored four goals in as many matches for America in the Apertura championship which began last month, would sign his contract after passing a medical.
"(Jimenez) is a player with an enormous future and who will complete our attacking line. He will give us very interesting options to face our goals this season," Atletico sporting director Jose Luis Perez told the club's website (www.clubatleticodemadrid.com).
Jimenez will be the third Mexican to play for Atletico Madrid after Hugo Sanchez (1981-85) and Luis Garcia (1992-94).