The 22-year-old, who has a child with Diego Maradona's daughter, extended his contract to 2014 in January but his buy-out clause was reduced from 60 million euros to 45 million, prompting speculation about a possible exit.
"I have thought about it a lot and I am convinced I must be true to myself," Aguero said on his personal website.
"I don't think I should impose a limit on the chance of continuing to learn and grow," he added.
"After five intense years a stage in my personal development has ended and I have to move on to a new one."
Atletico's majority-shareholder Miguel Angel Gil said in January that offers from Tottenham and Chelsea for Aguero, who joined from Independiente in 2006, had been rejected.
Atletico missed out on next season's Champions League, qualifying for the continent's second-tier club competition, the Europa League, which they won in 2010.
