The Brazilian scored 20 goals last season as Los Rojiblancos finished third in La Liga and claimed an historic victory over neighbours Real Madrid to lift the Copa del Rey.
His performances had attracted attention from clubs around Europe with Liverpool reportedly trying to activate the buy-out clause in his previous contract with a bid in the region of €24.5 million (£21 million) last week.
However, the 24-year-old insisted that he is delighted to have extended his deal with Atleti.
“I am very happy with this deal after fighting for a long time to win the affection of the fans, my team-mates and people inside the club,” he told the club’s website. “It is a very special moment and I am very happy here.
Costa is expected to have an even more prominent role this season as Atletico return to UEFA Champions League action after a four-year absence without their top-scorer for the past two seasons Radamel Falcao, who joined Monaco for €60 million back in June.
Atletico get their La Liga campaign underway on Sunday night when they travel to face a new-look Sevilla side.