Burak was born in Istanbul but grew up and attended school in Izmit, as his parents divorced and he lived with his mother and grandfather. In 2014, Burak lost his mother to an incurable disease. This was a devastating blow. Since childhood, Burak had watched films and put himself in the shoes of the characters, always wanting to be on the other side of the screen. This desire brought Burak to Istanbul, and his entire family supported his decision, standing behind him. Having made this decision, Burak began reading a lot, watching films, observing, and taking acting lessons, which he continues to do. His manager, Gökçe Doruk Erten, has guided and supported Burak since the beginning and continues to this day.

Burak studied at the University of Arts. His acting career began in 2011 with the series "College Life." In this series, he played the role of Onur. Özge Çelik and Furkan Andıç also starred in the series. Then, in 2012, he starred in the series "Sultan" alongside Nurgül Yeşilçay. In 2013, Burak Deniz starred in the series "The Fugitive." His role as Burak Topçuoğlu already marked his rise to popularity. In that series, he starred alongside actors such as Görkan Uygun, Berk Hakman, Begüm Birgören, and Yağmur Tanrısevsin. In 2015, Burak joined the popular series "Tide" in episode 65, playing the role of Aras. Cagatay Ulusoy and Serenay Sarıkaya also starred in the series. He enjoys playing villains. He played a lot of computer games as a child, and he still plays; it's a favorite hobby he can't give up. He prefers playing war games. His favorite color is green. He doesn't have a specific favorite song. He enjoys instrumental music and listens to a lot of foreign songs. He doesn't play sports, but he once played hockey, but quit due to lack of time.

His favorite foods are meat, dolma, and spaghetti. He's not picky and enjoys a good meal. He's been dating actress Bushra Develi since 2015. Bushra and Burak's relationship began on the set of the TV series "Pretty Little Liars." Three years later, in 2018, they broke up.

At the end of 2020, he began dating supermodel Didem Soydan.