On 20 July 2015, Savić moved to Atlético Madrid for €10 million fee and signed a five-year contract with the club; midfielder Mario Suárez moving in the opposite direction for free as part of the deal, though Suárez later sold for €4 million in January 2016. Savić became the first Montenegrin footballer who played in the Champions League final in the 21st century, 18 years after Predrag Mijatović, who scored decisive goal in the 1998 final for Real Madrid against Juventus.