Asmir Begovic was born in Trebinje, Bosnia and Herzegovina, which was at the time part of Yugoslavia, to a Bosniak family. His father, Amir, was also a goalkeeper who played for Leotar and Iskra Bugojno whilst his mother, Ajnija, hails from Stolac. The Begović family fled the Bosnian War to Germany when Asmir was four years old, where he began to play organised football with local youth club FC Kirchhausen in Heilbronn. When he was 10, his family moved to Edmonton in Canada.
Begovic attended the St. Francis Xavier High School where he played for their academy. He also played Minor League Soccer with the Southwest Sting Soccer Club in Edmonton which earned him a call-up to the Canada under-17 squad. In 2003, he earned a trial with Portsmouth and Tottenham Hotspur and his representatives paid for him to fly over to England. After two days with Portsmouth, coaches David Hurst and Mark O’Connor were suitably impressed and offered Asmir Begovic a contract before his trial at Tottenham could begin.
Begovic signed a youth contract with Portsmouth in the summer of 2003 and due to him not having a European Union passport he spent two years on an education visa which prevented him from featuring in matches which involved money being taken on the gate. After playing for the youth team he then spent time on loan at La Louviere in Belgium in 2005 where he played twice in the Belgian top flight. Asmir Begovic got his UK visa in the summer of 2006 which allowed him to sign on loan for Macclesfield Town in the 2006–07 season, making his Football League debut in a 1–1 draw at Stockport County on 25 November as an 80th minute substitute, after injury to first choice goalkeeper Jonny Brain. His loan spell was cut short, however, as he sustained a knee injury after making just three appearances. In August 2007, Begović was loaned to AFC Bournemouth in League One in a deal lasting until January 2008. He was recalled back from Bournemouth on 11 October 2007. On 8 December 2007, Begović was named in Portsmouth’s 16-man matchday squad for the first time in a Premier League game in a match against Aston Villa as a substitute.
In March 2008, he signed for Yeovil Town on loan for a month with Portsmouth having the right to recall him back when they so desired. On 29 March Asmir Begovic made his debut for Yeovil, keeping a clean sheet against Bristol Rovers. He was subsequently recalled after making two appearances despite Yeovil trying to re-sign him on an emergency loan. The “Glovers” manager Russell Slade revealed in June 2008 that he wanted to sign Begović on loan again after Steve Mildenhall joined Southend United. The move was delayed however due to his grandfather passing away. He rejoined Yeovil on loan, this time for three months in August 2008. He made 14 league appearances, keeping three clean sheets in a struggling Yeovil side.
Begović made his Portsmouth debut against Sunderland in their 3–1 win on 18 May 2009. Following his Premier League debut for Pompey Begović expressed his delight. “It was fantastic, to make your first Premier League appearance is something I’ve looked forward to for a long long time.” He joined Championship team Ipswich Town on loan until 16 January 2010 in October. On 23 November Asmir Begovic was recalled to Portsmouth due to David James being injured, ending his Ipswich Town loan after having played six matches. On his return to Fratton Park he went on to play 15 first team matches during the 2009–10 season.
Begović playing for Stoke City in 2011
On 1 February 2010, Begović signed a four-and-a-half-year contract at Stoke City for a fee of £3.25 million. Following the signing manager Tony Pulis revealed that he had been tracking Begović for a while. “We have been tracking Asmir for some time and we believe that potentially he is the best young keeper in the country”. Begović had also held talks with Tottenham Hotspur prior to joining Stoke, but opted for the “Potters” due to “sporting reasons”. He later revealed his relief at leaving Portsmouth following their financial turmoil during the 2009–10 season. Portsmouth ended up owing Tottenham money for Asmir Begovic , despite him turning them down, as Tottenham had already paid Portsmouth an instalment on the transfer. Portsmouth were ordered to pay Tottenham £1 million by the Premier League over the aborted transfer as Spurs had already made an initial payment for both Begović and Younès Kaboul.
Begović made his debut for Stoke against Chelsea on 25 April 2010, replacing the injured Thomas Sørensen in the 35th minute, where he conceded five goals. He kept his first clean sheet for City in a 0–0 draw with Everton on 1 May 2010. He also played in the last two games of the 2009–10 season against Fulham and Manchester United.
At the start of the 2010–11 season Begović was handed the number one jersey by manager Tony Pulis. Begović allegedly refused to play in a League Cup match against Shrewsbury Town, a decision which Pulis said was “totally disrespectful”. Asmir Begovic on the other hand, denied that he had refused to play. Despite this Begović played his first match of the season in the next round of the League Cup against Fulham and then West Ham United. He made his first league appearance on 30 October against Everton replacing the injured Sørensen. Following this Begović took over from Sørensen as City’s first choice ‘keeper, he also ‘made peace’ with Tony Pulis with his absence from the Shrewsbury match. After a narrow defeat at Arsenal in February 2011 Begović believes that Stoke are developing well. The following week against West Ham, Asmir Begovic made an error gifting a goal to Demba Ba. Begović missed out on an FA Cup Final with second choice ‘keeper Sørensen being preferred to play in cup matches.
Begović started the 2011–12 season as first choice keeper and earned praise from Tony Pulis after he kept five clean sheets in six matches including a fine display against Liverpool on 11 September. However, Begović then conceded eighteen goals in the next seven matches, including a woeful 5–0 defeat by Bolton Wanderers a performance which led him to apologise to the supporters for his display.Following the Bolton match he was dropped in favour of Sørensen. Begović signed a new four-and-a-half year contract extension with Stoke in December 2011 keeping him at the club until 2016. He regained number 1 spot in March 2012. Begović continued as City’s number one stopper in 2012–13 and began the season in fine form conceding just 12 goals in the opening 15 matches. Despite Stoke having a poor second half to the season, Begović remained in decent enough form and won the Player of the Year Award.
Begovic remained first choice ‘keeper going into the 2013–14 season under new manager Mark Hughes and produced a man of the match performance on the opening day against Liverpool. On 2 November 2013, Begović scored after 13 seconds against Southampton at a distance of 97.5 yards, after his long kick downfield deceived Artur Boruc. His goal against earned him a place in the 2015 Guinness World Records for the ‘longest goal scored in football’.
On 13 July 2015, Chelsea signed Begović on a four-year deal for a fee of £8 million. As part of the deal Chelsea also offered midfielder Marco van Ginkel in part exchange to Stoke on loan for one season.
He made his debut nine days later on Chelsea’s pre-season tour, coming on at half time for Thibaut Courtois with Chelsea 1–0 up against the New York Red Bulls, but the match ended in a 2–4 defeat. Manager José Mourinho defended Begović’s performance, attributing it to fatigue. His first competitive fixture was the 2015 FA Community Shield on 2 August at Wembley Stadium, in which he was unused in a 1–0 loss to rivals Arsenal. Six days later he came on as a substitute for Oscar when Courtois was sent off for conceding a penalty with a foul on Bafétimbi Gomis, who converted it for a 2–2 draw. On 16 August, Begović made his first competitive start for Chelsea in a 3–0 away loss to Manchester City. A month later, he earned the first clean sheet of the season for Chelsea in a UEFA Champions League match against Maccabi Tel Aviv which ended in a 4–0 win for Chelsea. He kept a sequence of three clean sheets before Courtois returned to the team on 5 December.
In his second season with Chelsea, Asmir Begovic didn’t get much playing time, and there were speculations that he would leave the club in the winter transfer window. However, since Chelsea couldn’t find a replacement for him, he was forced to stay at Stamford Bridge. In spite of featuring in only two league games, he received a winners’ medal as Chelsea won the 2016–17 Premier League.
On 30 May 2017, Begović signed for Premier League club Bournemouth on a long-term contract for an undisclosed fee. He debuted for Bournemouth on the opening day of the new Premier League season, in a 0–1 loss against West Bromwich Albion. Begović kept his first clean sheet in the season on 30 September, in a 0–0 draw against Leicester City. He had another impressive performance, this time against his former club Chelsea, which Bournemouth won 3–0.
On 2 September 2019, Begović was sent on a 6-month loan to Qarabağ. He made his debut for Qarabağ on 15 September 2019, in a 2–0 victory against Neftçi in the Azerbaijan Premier League.
He signed on loan for Milan for the rest of the 2019–20 season on 13 January 2020.