Erkin graduated from Galatasaray High School. He passed the examination and was sent to Paris, France for his education with Cezmi Rifki Erinc and Ekrem Zeki Un by the state in 1925. He studied in the Paris Conservatory and the Ecole Normale de Musique.
Upon his return to Turkey in 1930, he began teaching at the Musiki Muallim Mektebi (Music Teachers School). He met his wife Ferhunde Erkin at the Musiki Muallim Mektebi and married in 1932.
He shared the grand prize of the Cumhuriyet Halk Partisi with Ahmet Adnan Saygun and Hasan Ferit Alnar in 1943. He won the prize for his piano concerto. He wrote the famous Köçekçe orchestra suite the same year. In an interview he said that Alfred Cortot gave him the idea of composing a piano concerto during his visit to Turkey.
The same piano concerto and Köçekçe suite was premiered by the Presidential Symphony Orchestra on 11 March 1943. The orchestra was conducted by Dr. Ernst Praetorius, and Ferhunde Erkin was the soloist. On the request of Ambassador Franz von Papen, the piano concerto was performed in Berlin, Germany on 8 October 1943. The Berlin City Orchestra was conducted by Fritz Zaun and the soloist was again Ferhunde Erkin.
Erkin was awarded with the Palm Academique, Légion d’honneur chivalarous and official degrees, and the Italian Republic Medal. He was named a state artist by Turkey in 1971 and was awarded a medal of honor by the Sevda-Cenap And Music Foundation in 1991. A postage stamp commemorating his life was issued by the Turkish postal system in 1985.