After a successful start at Neuchâtel Xamax having scored eight goals in 17 games, Gavranović left his team to sign for Schalke 04 on 1 February 2010. He scored a vital goal for Schalke 04 in the Round of 16 in the Champions League against Valencia, which led his team to a 4–2 victory and a place in the quarter-finals. Gavranović joined fellow Bundesliga side Mainz on a season-long loan deal on 31 August 2011. Mainz reportedly paid €200,000 to secure his services and the loan included a deal for a permanent transfer worth €1.5 million.

Gavranović represented Switzerland on U-21 level in 14 games and scored three goals. On 26 March 2011, he made senior team debut in the 0–0 draw with Bulgaria in a Euro 2012 qualifier. His first goals arrived in a brace scored in a 4–2 friendly win over Croatia on 15 August 2012.

After only making five appearances during his loan spell, Gavranović returned to Schalke at which point he agreed to cancel his contract in May 2012 and moved on a free transfer to FC Zürich in the summer. He made his debut for Zürich on 15 July 2012, and scored his first goal from the penalty spot in the same match, a 1–1 draw with FC Luzern.

Gavranović scored Zürich’s winning goal against reigning champions FC Basel on 11 August 2013 in the fifth round of the Swiss Super League. He scored Zürich’s first goal as the club twice came from behind to defeat FC Stade Lausanne Ouchy 3-2 in the second round of the Swiss Cup on 15 September. On 24 November, Gavranović netted twice in the second half of Zürich’s Super League clash with FC Sion, inspiring his side to a 4–1 victory.

In the Zürich Derby match against Grasshoppers on 1 March 2014, Gavranović scored a goal in either half to give Zürich a 3-1 win. On 21 April 2014, Gavranović scored twice in extra-time to lead Zürich to a 2–0 victory over Basel in the final of the Swiss Cup.

Gavranović was named in the final 23-man squad for the World Cup in Brazil on 13 May 2014. On 29 June, he sustained a serious knee injury in training, ruling him out for the rest of the World Cup and until early 2015.

On 18 January 2016, Gavranović moved to HNK Rijeka in Croatia. He signed a 2 ⁄2-year contract with the club and joined their pre-season training camp in Dubai. Gavranović scored on his official club début on 12 February 2016, converting a cross by Roman Bezjak in the 25th minute to double Rijeka’s lead against Lokomotiva. In two years with the club Gavranović scored 40 goals in 80 appearances.

On 5 January 2018, Gavranović joined Dinamo Zagreb as part of player exchange deal involving Domagoj Pavičić and Luka Capan. He signed a 3-year contract with the club and selected the number 11 jersey. With a move to the new club and a successful spring season, Gavranović was determined to secure a place in Switzerland’s squad for the 2018 FIFA World Cup in Russia. During his official presentation in Zagreb Gavranović revealed that all of his family members are Dinamo supporters and since the early age he was also encouraged to support the club.

Gavranović is an ethnic Bosnian Croat, hailing from Gradačac. As of 2016, Gavranović is married to Anita, a Bosnian Croat from Derventa. In May 2019, Anita gave birth to a baby girl whom they named Leonie.

He was released from Dinamo at the end of his contract on 30 July 2020. However, he returned to the club just three weeks later due to injury of club’s first striker Bruno Petković. On 17 October, he scored his first hat-trick for Dinamo as they defeated Gorica 3–2.