Özbek cemented his spot as a solid regular starter at Galatasaray in his first season after an impressive start to the season. He recently celebrated the league title in Istanbul with his club. They won the 2007–08 season. At the start of the 2009–10 season, he scored a brace during the third qualifying round of the Europa League, against Maccabi Netanya on 6 August 2009. Özbek has adopted the nickname Barış for his commitment when it comes to chasing the ball.
His brother, Ufuk is also a professional footballer. Özbek is known to be fairly clumsy, during the renovation of his house in Trabzon, he managed to injure himself to miss the first half of the Turkish Premier Division 2011–12 season.