Savić began his professional career withBSK Borča during the2008–09 season. In early 2010, he was on a ten-day trial withArsenal. According to Savić, he had agreed to join Arsenal in the summer, but the transfer never went through.[7]
On 29 August 2010, it was announced that Savić had signed forPartizan on a four-year contract and was given the number 15 shirt.[8] He made four appearances in the2010–11 UEFA Champions League group stage and helped the club win the double.
On 6 July 2011, Savić signed a four-year contract forManchester City in a£6 million deal.[9][10] He made his debut againstSwansea City on 15 August as a substitute at theCity of Manchester Stadium. On 1 October, he came off the bench and scored his first goal for the club in a 4–0 victory away toBlackburn Rovers, heading in the conclusive goal from a corner fromSamir Nasri.
Throughout centre-backVincent Kompany's four-match ban from 11 to 25 January, Savić replaced him in the starting line-up, with third-choiceKolo Touré away on international duty with theIvory Coast in the2012 Africa Cup of Nations.[citation needed] Although Savić showed brief flashes of form in this time, he showed many instances of nervousness resulting in frequent misplaced passes, clearances and crucially conceded a penalty againstLiverpool in aLeague Cup match, resulting in a Liverpool win.[11] Via a poor first touch, he causedJermain Defoe's goal in City's 3–2 win overTottenham Hotspur.[12] With Kompany's return to the starting team, Savić returned to the bench. He ended the season with 12 league appearances, enough for a medal, as Manchester City won the2011–12 Premier League on the last day of the season.[13]
On 31 August 2012, ItalianSerie A clubFiorentina signed Savić as part of a deal forMatija Nastasić to transfer the other way. He was given the number 15 shirt and made his Fiorentina debut on 7 October, playing the full 90 minutes in a 1–0 win overBologna, and in December he scored his first two goals in a 2–2 home draw withSampdoria.[14] He finished the season with 26 league appearances and oneCoppa Italia appearance, helping Fiorentina to finish in fourth place in the2012–13 Serie A, thereby securing aUEFA Europa League place for2013–14.[citation needed]
Savić continued to be a mainstay in the Fiorentina defence in the2013–14 season, making 31 appearances in the league as Fiorentina again finished in fourth place.[citation needed] Savić made four appearances in the Europa League proper and two more in qualifying as Fiorentina made the last 16 of the competition, being beaten 2–1 on aggregate by rivalsJuventus.[citation needed] He also played both matches in theCoppa Italia semi-final win overUdinese and in thefinal, where his side lost 3–1 toNapoli.[15]
In the2014–15 season, Savić reached the milestone of 100 appearances for Fiorentina in all competitions.[citation needed] He was a major part of their run to the semi-finals in the2014–15 Europa League and the third consecutive fourth-place finish in Serie A, making 41 appearances in all competitions.[citation needed]
On 20 July 2015, Savić moved toAtlético Madrid for €10 million fee and signed a five-year contract with the club;midfielderMario Suárez moving in the opposite direction for free as part of the deal, though Suárez later sold for €4 million in January 2016.[16][17] Savić became the first Montenegrin footballer who played in theChampions League final in the 21st century, 18 years afterPredrag Mijatović, who scored decisive goal in the1998 final forReal Madrid against Juventus.[citation needed]
Stefan's father Dragan was the president of the municipal assembly inMojkovac when he committed suicide on 6 April 2011 when Stefan was 20 years old.[21] Subsequently,Red Star Belgrade'sDelije ultras, who are otherwise not known for being sympathetic to people associated with crosstown rivals Partizan, held up a banner[clarification needed] which said "Support for Stefan Savić" after the loss of his father.[22]