He was born in 1992 in the Alanya district of Antalya. He completed his high school education at Aldemir Atilla Konuk Anatolian High School. He went to Istanbul for higher education and studied at the Istanbul Bilgi University Business Administration Department. During his university years, he took acting lessons from Altan Gördüm at the Academy 35 Buçuk Art House.

His acting career began with a role in the fantasy series Sana Bir Sır Vermeyecek (2013-2014). He became known for his character "Tilki" in this series. The series was broadcasted for 29 episodes. He continued his acting career with the series Benim Adım Gültepe (2014). The series lasted for 8 episodes. He continued to appear on screens with the series Muhteşem Yüzyıl Kösem (2015), in which he portrayed the 14th Ottoman Sultan Ahmet I. Koç appeared in 26 episodes in the series. He took the leading role as "Burak Özer" in the series Hayat Sırları (2017). The series was broadcasted for 11 episodes. Bozkır (2018), in which he portrayed the character "Nuri Pamir", is Koç's first digital project. The series was broadcasted for 10 episodes on BluTV. In 2020, he was highly appreciated for his series Uyanış: Büyük Selçuklu, in which he portrayed the Great Seljuk Sultan Ahmet Sencer. Koç appeared in 34 episodes of the series. He guest starred in Succession, which was broadcast in the USA, as the character "Kadir".

His first movie role was in Senden Bana Kalan (2015), in which he shared the leading roles with Neslihan Atagül. Later in the cinema, he portrayed the character of "Mehmed" in the film Ali ve Nino, adapted from Kurban Said's Ali ve Nino, and Halis Karataş in the film Bizim İçin Şampiyon (2018). He played the leading roles in the films Okul Tıraşı, directed by Ferit Karahan, and Kurak Günler, directed by Emin Alper.

He played the leading role as Efe Tekin in the TV series Üç Kuruş, produced by Ay Yapım, which started broadcasting in 2021. The series has been broadcasted for 28 episodes.

In 2022, he appeared at the Cannes Film Festival with his films School Shave, Dry Days and The Great Flight, in which he played the leading role.