[3] Özyakup began his career at Zaandam Türkspor, a local amateur club which Dutch players with Turkish descent were predominantly recruited, where he later caught the attraction of AZ officials.

[8][9][10] On 28 August 2011, Özyakup was named a substitute for the Premier League match against Manchester United in which the London-based club suffered a heavy 8–2 defeat.

[17] Özyakup was an unused substitute in the UEFA Champions League round of 16 tie to Milan, which Arsenal won 3–0 on the night but lost 4–3 on aggregate.

On 29 August 2013, he scored his first goal at European competitions at 2nd leg of play-off round of 2013–14 UEFA Europa League encounter up against Norwegian outfit Tromsø IL, ended 2–0 for favour of Beşiktaş.

[22] He recovered from his injury, returned onto field on match day 9 encounter against Akhisarspor at Manisa 19 Mayıs Stadium, ended 3–3 in which he scored the 2nd goal of Beşiktaş.

[33] On 22 October 2015, Özyakup assisted Mario Gómez on UEFA Europa League group stage week 3 game against FC Lokomotiv Moscow, ended 1–1.

[35] He represented the captaincy of Beşiktaş for the first time, as a part of starting line-up at Turkish Cup quarter finals encounter away against Konyaspor, ended 1–0 for home side, on 3 March 2016.

Özyakup scored the opener with reportedly "elegant" dribbling combinations, passing his opponents, including goalkeeper Haydar Yılmaz on 1st match day encounter of 2016–17 season, ended 4–1 for Beşiktaş at Vodafone Arena, on 20 August 2016.

[7][11] On 29 January 2020, it was announced that Özyakup joined Eredivisie side Feyenoord on loan until the end of the 2019-20 season, taking the shirt number 18.

[52] He immediately scored in his debut for the club in the 71st minute of a 1–1 league draw against NEC on 10 September, a strike from distance assisted by compatriot Burak Yılmaz.

[65] He is "skillful" at finishing and possesses a high level of anticipation that allows him to be at the right place on the pitch, according to former Beşiktaş and Turkish international forward Feyyaz Uçar.

[68][69] Dilmen also said that Özyakup was an "intelligent" player, praised his "Zinedine Zidane-like" dribbling attributes and claimed that he was talented enough to play for Barcelona.

[73] After falling out of favor with the then coach Şenol Güneş during the 2018/2019 season, TV pundit Ali Ece claimed on a YouTube show that Özyakup was receiving mental health assistance from sports psychologists.

While the public and the rest of the sports media generally agreed that Ece crossed a line in disclosing private information, Özyakup nonetheless denied the claims and sued him for slander.