Behich played in the junior divisions ofGreen Gully SC.[6][7] He participated in the junior leagues of Melbourne's North-West. He had played for the club's Reserve team in 2007.[8] In February 2007 Behich had returned to Australia after having been training at theDavid Beckham Academy. In 2008 Behich was signed to the club's first team, surprisingly because the coach; Ian Dobson, had preferred experienced players within his squad, where he made his debut on 22 February 2008 in a 2–0 loss againstRichmond. He had been substituted onto the field in the 57th minute. He had been promoted to the club's first team with teammateDiogo Ferreira, who also went on to sign for Melbourne during Behich's second youth season.In 2008, Behich scored two goals in 11 appearances while playing for Green Gully in Australia's Second Division.[9] He had scored his two goals in a 6–1 win against Fawkner Blues on 17 May 2008, he had been substituted onto the field in the 76th minute and scored in both the 84th and 86th minutes.[9]
Prior to the start of the 2008–2009 A-League's National Youth League, Behich was selected for Melbourne Victory's squad.[10][11][12] On 3 January 2009, Aziz scored in a 3–0 win againstQueensland Roar.[13] One week later, he scored again in a 2–0 win againstPerth Glory on 10 January 2009.[14] Victory went on to finish in 6th position out of seven teams.
During the National Youth League's off-season, Behich would return to play for Green Gully in the 2009 season.[15][16] Aziz had appeared 22 times for Green Gully, once in the final's play-offs, and had scored two goals overall. His second goal came in a play-off match againstAltona Magic where which Behich was substituted onto the field in the 80th minute when Green Gully were trailing 3–2. Behich had scored an equaliser in the 94th minute to take the game to extra-time, however, Green Gully eventually lost 4–3 on penalties[17][18]
The following season, Behich was the only youth player to re-sign with Melbourne's youth team and was handed the captain's arm band.[19][20][21][22]
Behich made his debut forMelbourne Victory's first team on 16 January 2010, in the2009–10 A-League season, where he was substituted on to the field in the 83rd minute forCarlos Hernández in a 6–2 win against Perth Glory.[23] His second appearance was on 23 January 2010, where he was substituted onto the field in the 91st minute, again for Carlos Hernández, in a 2–0 win againstAdelaide United.[24] Despite Matthew Theodore being the only player to sign from Melbourne's youth-team to its first team in 2009, as of 2010 Behich was the only youth player to gain a first-team appearance and consecutive first-team appearances. It was then announced, in January 2010, that Behich was named in Melbourne's2010 AFC Champions League squad.[25] He was substituted on during the second half of the 2009–2010 A-League Grand Final when Melbourne lost on penalties to Sydney, and is notable for the narrowest miss of the match, which could have been the winner. Behich then signed to Hume City in the Victorian Premier League during the A-League off-season.
Behich debuted for Hume City in a 2–2 draw againstNorthcote City on 16 May 2010. Scoring on debut, he netted Hume city's second goal on 81 minutes. He appeared 5 more times for the side, departing from the club in June, as they finished in second spot of theVictorian Premier League table.[26][27]
By July 2010, he trialled with the Melbourne Heart squad where he took part in a round of warm up matches that the club played, including a 2–0 defeat againstEverton. Behich, shortly after trialling with Melbourne Heart, signed a seven-week deal with the club as an injury replacement player for Kristian Sarkies until October 2010. AfterDean Heffernan received a red card, Behich slotted into the starting lineup to cover his position, and started most games afterwards. On 25 October 2010, he signed a full-time contract with theMelbourne Heart, becoming the first player to play for both Melbourne Victory and Melbourne Heart.[28] At Heart, he was developed into more of a defensive player, a left back or left winger, as opposed to the striker position he played at Victory. He was the first player to be sent off in aMelbourne derby, given his second yellow in the very first encounter between the clubs, which Heart won 2–1. In January, Behich was awarded the A-League Young Footballer of the month.[29] It was reported on 28 January 2012 by the Dutch media that Behich had attracted the interest ofEredivisie clubExcelsior and2. Bundesliga sidesVfL Bochum andEintracht Frankfurt. Excelsior managerJohn Lammers spoke of his interest in the exciting youngster toRotterdam newspapersAlgemeen Dagblad andNRC Handelsblad:[30][31] "We are looking to bring Aziz to the club, he's an exceptional talent who we've been watching."[32]
On 29 January 2013, Behich signed to TurkishSüper Lig clubBursaspor.[33] On 11 March 2013, Aziz Behich made his TurkishSüper Lig debut for Bursaspor against Fenerbahçe as a 69th-minute substitute forTuncay.[34] On 4 March 2016, Behich signed three-year extension to his contract with Bursaspor, which was due to expire in May.[35]
On 31 August 2018, Behich signed forEredivisie clubPSV Eindhoven for four years. The transfer fee paid to Bursaspor was reported as for $4.5 million[36]
After parting ways with Dundee United, Behich signed a two-year deal for Melbourne City on 6 August 2023.[41] This marked his return to the club after nine years overseas.
On 31 January 2024, while onAsian Cup duty with the Socceroos, he joinedAl-Nassr on loan for the remainder of the 2023–24 season.[42] The loan fee was reported to be around $2 million AUD.[43]
Behich was called up to the Australia Under-23 side by coachAurelio Vidmar for a friendly match against Japan's Under-23 side at the Tohoku Denryoku Bigswan Stadium, Niigata on Wednesday 1 June 2011.[44] Behich was selected to play against Yemen's under-23 side for theFootball at the 2012 Summer Olympics – Men's Asian Qualifiers Preliminary Round 2. On 14 June 2011, in preparation for the2012 AFC Men's Pre-Olympic Tournament, Behich featured in a 6–0 win against Singapore under-23 where he scored Australia's sixth goal in the 90th minute. On 19 June 2011 Behich played in Australia's first-leg 3–0 win against Yemen.[45][46][47][48] Four days later he played in the second leg which resulted in a 4–0 win to Australia on 23 June.[49]
Behich was called up to the Australian national team byHolger Osieck for a friendly match againstSouth Korea on 14 November 2012, where he made his debut.[50]
Behich was also called up to the Australia squad by managerGraham Arnold for the2022 FIFA World Cup where he started all 4 matches during Australia's campaign to the Round of 16.[51] Behich made a run pastArgentinian defenders and had a chance at an equalising goal in the dying seconds of theRound of 16 game, but his shot was stopped byEmi Martinez.[53] Behich was also a prominent member of Australia's squad in the2023 AFC Asian Cup and all rounds of the2026 World Cup qualifiers.
Behich is a Muslim ofTurkish Cypriot origin, son of immigrants to Australia fromCyprus.[54]For this reason he was eligible to represent Turkey, Cyprus or Australia, eventually choosing the latter.