During the 2011–12 Premier League season, Džeko scored four goals in one game for Manchester City against Tottenham Hotspur at White Hart Lane.

Džeko became the highest Bosnia and Herzegovina goalscorer of all time on 7 September 2012 in a game against Liechtenstein, scoring a hat-trick to surpass Zvjezdan Misimović and Elvir Bolić.

[14] On 14 June 2022, by playing against Finland in a 2022–23 UEFA Nations League B game, he became his country oldest player at 36 years and 2 months, beating Samir Muratović record.

[15] On 7 September 2024, by scoring a goal against Netherlands in an 2024–25 UEFA Nations League A game, he became Bosnia and Herzegovina oldest goalscorer at 38 years and 5 months, surpassing Emir Spahić record.

[21] After moving to Wolfsburg, Džeko scored five goals and recorded three assists in his first 11 games: he was named by Sportal as the best striker in the first half of the 2007–08 Bundesliga season.

[22] After Wolfsburg acquired fellow Bosnian international Zvjezdan Misimović in July 2008, Džeko's performances improved significantly.

[23][26] Wolfsburg ended the season as Bundesliga champions for the first time in the club's history; they finished two points clear of Bayern Munich, the key match being the meeting between them on the 26th matchday which finished 5–1,[27][28] Džeko and Grafite scoring two goals each in an impressive performance (the latter added his second and the team's fifth with a memorable dribble and backheel).

[23][26] At that point Wolfsburg, in third at the start of the day, gained the lead in the table for the first time[29] and retained the position for the rest of the season to take the title.

[36] On 28 August 2010, Džeko became the top league scorer in Wolfsburg's history with 59 goals in 96 appearances, surpassing Diego Klimowicz who scored 57 in 149 games.

[41][42][43] The previous ex-Yugoslav record stood for more than a decade – the transfer fee paid by Real Madrid to Fenerbahçe for Elvir Baljić in 1999 (€26 million).

[46] He made his debut for the club in a 4–3 win over Wolverhampton Wanderers on 15 January in which he set up Yaya Touré for the third goal of the match.

[47] Džeko marked his FA Cup debut on 30 January 2011 with the equalising goal in Manchester City's fourth round match against Notts County which ended in a 1–1 draw.

[49] Džeko scored twice against Aris Thessaloniki within four and a half minutes at the Etihad Stadium in the second leg of the last 32 of the UEFA Europa League on 24 February 2011.

[65] On the opening day of the 2013–14 Premier League season, Džeko was selected to start by a new manager Manuel Pellegrini against Newcastle United at the City of Manchester Stadium.

[67] On 27 April, he scored City's first goal of a 2–0 defeat of Crystal Palace at Selhurst Park, closing the gap on league leaders Liverpool to three points with a game in hand.

[72] On 24 September, Džeko scored his first two goals of the season as Manchester City beat Sheffield Wednesday 7–0 in the third round of the Football League Cup.

[78] He made his Serie A debut ten days after his move from Manchester City, playing the entirety of a 1–1 draw at Hellas Verona,[79] and in his second appearance on 30 August, he scored the winning goal in the 79th minute to defeat reigning champions Juventus 2–1 at the Stadio Olimpico.

[95] Džeko also helped Roma reach UEFA Champions League quarter-finals by scoring the winning goal against Shakhtar Donetsk.

[126] On 22 June 2023, Süper Lig side Fenerbahçe announced that Džeko arrived in Istanbul to complete his transfer to Turkey.

[128][129] A month later, on 26 July, he made his debut for the club as the captain, in which he scored a goal and provided two assists in their 5–0 win over Zimbru Chișinău in the Europa Conference League second qualifying round, becoming at 37 years Fenerbahçe oldest player and goalscorer in European competitions.

[130] On 13 August, he made his Süper Lig debut against Gaziantep at the Şükrü Saracoğlu Stadium, scoring both goals in a 2–1 win for Fenerbahce.

[132] He concluded his debut season as Fenerbahçe's top scorer with 21 goals, ranking second in the league, just behind Mauro Icardi.

On 23 July 2024, he made his season debut against Lugano in an UEFA Europa League second qualifying round away game, scoring a hat-trick in a 4–3 win for Fenerbahce.

[137] Džeko ended the 2014 FIFA World Cup qualification campaign as second-top scorer with ten goals as Bosnia and Herzegovina qualified for the first major tournament in its history.

[140] On 25 June with the team already eliminated, in the final group match against Iran, Džeko scored the opening goal to help Bosnia and Herzegovina to their first ever FIFA World Cup win.

[141] In August, following the retirement of Emir Spahić from the international team, manager Safet Sušić named Džeko the new captain.

[143] On 13 November 2016, Džeko had an altercation in a 2018 FIFA World Cup qualifier against Greece with Greek player Kyriakos Papadopoulos, in which he pulled down Sokratis Papastathopoulos' shorts while trying to obtain the ball.

[147][148] Considered by pundits and managers to be one of the best strikers in Europe, although he is mainly known for his goalscoring abilities, he is also a generous player, who has a penchant for providing a good number of assists in addition to scoring many goals.

[151] His former Roma manager Luciano Spalletti once described him as the "perfect prototype" of a striker, noting that he is "strong, tall, fast for his height, combative, aggressive and has good technique.

[152] During his time with Manchester City, he was considered a "super-sub", as he scored many important goals coming off the bench,[153] a label which he himself rejected on several occasions.