He started his career with Prva HNL side Hajduk Split in 2002, before moving to Belgian Pro League club Zulte Waregem in 2007. A year later, he moved to Austrian Bundesliga club Rapid Wien. In 2010 he was signed by Scottish club Rangers, with whom he won the Scottish Premier League and the Scottish League Cup before joining Everton in 2012.
Jelavić was born in Čapljina, SR Bosnia and Herzegovina, SFR Yugoslavia and started his youth career at his local side GOŠK Gabela, which plays in the Bosnian league system. His career took a more serious turn when he moved to the nearby cross-border club in Croatia, NK Neretva from the town of Metković, managed by Branko Gutić. At the encouragement of Ante Prco, Ivan Gudelj, Dražen Mužinić and Vilson Džoni he was brought to Hajduk Split's junior side at the age of 15.
In the 2008–09 season, Jelavić played for the Austrian champions Rapid Vienna. In the Austrian Bundesliga he played 24 games (as first squad in 9 and as substitute in 15) and scored 7 goals without any yellow or red cards. In 2009–10, in the Austrian Bundesliga, he played in 33 games (as first squad in 31 and as substitute in two) and scored 17 goals with 5 yellow cards and 1 red card. In the Europa League, he played six games and scored four goals with one assist.
In the summer of 2010 Jelavić was linked with a transfer to Rangers. A fee was originally agreed between the two clubs on 26 July, but the transfer was delayed by a dispute between the player and Rapid Vienna over a payment Jelavić claimed the club owed him. On 19 August, Rapid announced that Jelavić would be signing for Rangers, after the player announced he would not play in Rapid's Europa League qualifying match against Aston Villa.
On 20 August 2010, Jelavić completed a £4 million move to Rangers on a six-year-deal. He made his debut in a home match against St. Johnstone on 28 August 2010. Due to his former club Rapid Vienna eliminating Aston Villa from the Europa League, Jelavić was ineligible to participate in Rangers' Champions League campaign, after becoming cup tied after appearing for the Austrian side in the earlier rounds.
On 11 September, Jelavić scored his first Rangers goal against Hamilton Academical at New Douglas Park after he headed in a Kyle Lafferty cross. On 21 September, Jelavić played against Dunfermline Athletic in the League Cup, scoring two goals in the game including an overhead kick in a 7–2 win for Rangers. In Rangers next away match to Aberdeen at Pittodrie Stadium, Jelavic scored what turned out to be the winning goal in a 3–2 Rangers win. Rangers were 2–0 down before coming back to win the match with Jelavić scoring the third Rangers goal. The next week Jelavić was injured in a match against Heart of Midlothian at Tynecastle Stadium, suffering ankle ligament damage due to a tackle by Hearts midfielder Ian Black. Jelavić claimed that Black had intended to injure him, a charge denied by his opponent, who apologized for the challenge. He scored two goals in a match against Dundee United in October 2011.
After making his comeback off of the bench, Jelavić started his first match since his injury on 26 January 2011, scoring away from home against Hibernian in the first half. Jelavić's first hat trick for Rangers came in a 6–0 win over Motherwell on 12 February 2011 at Ibrox Stadium. In Rangers' 4–0 victory against St. Johnstone on 27 February 2011, Jelavić scored two goals and assisted a third with a backheel pass. On 20 March 2011, Jelavić scored the winning goal in extra time in Rangers' 2–1 win over Celtic in the 2011 Scottish League Cup Final. He then scored in consecutive away 1–0 victories over Hamilton Academical and Aberdeen. Jelavić rounded off the season by scoring five goals in the last six matches of the season including a goal and two assists in Rangers' 5–1 title winning victory against Kilmarnock on the last matchday of the season. Jelavić received the SFA goal of the season award for his goal against Aberdeen. Jelavic ended the 2010–11 season with the best goals to game ratio in Scotland after scoring 19 goals in just 27 starts, better than any other striker in Scotland.
On 22 July 2011, a day before Rangers opening match of the season against Heart of Midlothian, it was announced that Jelavić would wear the number nine shirt for the 2011–12 season he had previously worn the number 18. On 30 August 2011, it was reported that Rangers had rejected a £6.5m bid from Championship club Leicester City for Jelavić. Jelavić scored his first European goal for Rangers on 3 August 2011 in a 1–1 draw against Malmö in a UEFA Champions League qualifying game. On 5 November 2011 Jelavić scored his first brace of the season helping Rangers to a 3–1 victory over Dundee United. Jelavić scored another two goals in a 2–0 win over Hibernian on 10 December 2011. His third brace of the season came on 14 January 2012 in a 2–1 win over St Johnstone. Jelavić left Rangers having scored a total of 36 goals in a total of 55 appearances in all competitions. Jelavić playing for Rapid Vienna===Everton=== On 31 January 2012, Jelavić signed a four-and-a-half-year deal with Everton for a fee of £5 million. He made his debut a few days later, as a second half substitute for Denis Stracqualursi, in a 1–1 draw against Wigan Athletic at the DW Stadium. On 10 March 2012, Jelavić scored his first goal for Everton in his first start for the club, scoring the only goal of the game in a 1–0 victory against Tottenham Hotspur at Goodison Park. His first FA Cup goal was the opener in a 2–0 win against Sunderland in a quarter-final replay at the Stadium of Light. Jelavić scored his first brace for Everton against Norwich City in a 2–2 draw at Carrow Road in the Premier League. The following week he scored the opening goal in a 2–1 defeat by neighbours Liverpool, in the FA Cup semi-final at Wembley Stadium.
Jelavić scored twice in a 4–4 draw against Manchester United at Old Trafford, becoming the first Everton player to score in five successive away games since Duncan McKenzie in 1977–78. In scoring twice against Fulham he became the quickest player to reach 10 goals at Everton since Tom Browell in 1912. Jelavić was named the Premier League Player of the Month for April 2012, the first Croatian to achieve this. Jelavić scored his 11th goal for Everton against Newcastle United on the final day of the season and finished the season as Everton's top scorer both in the league and overall. He scored his first goal of the following season on 25 August 2012 in a 3–1 win against Aston Villa at Villa Park. Jelavić netted his first two home goals for the campaign against Southampton in a 3–1 win, these goals were also his first at the famous Gwladys St End at Goodison Park. Jelavić continued his scoring form in the next game against Wigan Athletic with a headed goal to make the score 1-1. Jelavić scored his next goal, the winner in a 2-1 win against Sunderland. His next goal came in stoppage time of a game against Tottenham Hotspur in a 2-1 victory at Goodison Park.
In 2007, Jelavić was called up for the Euro 2008 qualifiers, although he did not feature in any of the qualifying matches for the competition. Jelavić eventually made his full international debut in a friendly match against Qatar on 8 October 2009 in Rijeka, coming on as a substitute for Ivan Klasnić in the 64th minute in which he also scored his first international goal to secure his team a 3–2 win in the final moments of the match. On 14 October 2009, he made his first competitive international appearance for Croatia, in the team's final 2010 FIFA World Cup qualifier against Kazakhstan in Astana, again coming on as a substitute for Klasnić, in the 77th minute.
Jelavić was selected for Croatia's UEFA Euro 2012 squad. He scored his first competitive international goal and his country's second in their first group stage match against Republic of Ireland resulting in a 3–1 win. He also featured in Croatia's group stage matches against Italy and Spain but did not score and Croatia was eliminated after the group stage.
- Scores and results list Croatia's goal tally first.
|1.||8 October 2009||Stadion Kantrida, Rijeka||Qatar||3–2||3–2||Friendly|
|2.||11 August 2010||Štadión Pasienky, Bratislava||Slovakia||1–1||1–1||Friendly|
|3.||10 June 2012||Municipal Stadium, Poznań||Republic of Ireland||2–1||3–1||Euro 2012|
|4.||7 September 2012||Stadion Maksimir, Zagreb||Macedonia||1–0||1–0||2014 FIFA World Cup qualification|
Jelavic is married to Dajana Jelavic, whom he had started dating when he was 17 years old. Together they have two daughters, Nika and Lana. Jelavic also makes significant financial contributions to his boyhood club, GOŠK Gabela.
- As of match played 12 January 2013.