Mehmet Suphi was born to İsmail Zühdü and his spouse Emine in Açıktürbe quarter of Üsküdar, Istanbul, then Ottoman Empire, in 1869. His family name "Ezgi", he took after the adoption of the Surname Law in 1934, means ""melody".His father was an accounting controller at the Ministry of Post and Telegraphs of the Ottoman Government. Following the secondary education, he attended the Imperial Military Medicine School. He graduated in 1892 in the rank of Captain. Already at the age of five, he stood out while chanting in the neighborhood school. His father was an amateur singer and music instrument player, who arranged weekly musical meetings at home with music lover associates. Notable musicians of the era like Medeni Aziz Efendi, Hacı Arif Bey and Kemani Tahsin joined the meetings. Mehmet Suphi attended the meetings in the beginning by singing. At the age of eleven, he received his first music lessons in violin from Kemani Tahsin, adjutant major of the Imperial Military Music Band. During his education of medicine at the boarding school, he visited Medeni Aziz Efendi on weekends for musical tuition.
Ezgi played the tanbur, as well as the violin and the viola d'amore, and blew the ney. By singing, he had a special own style. He learned Western European musical notation from Hacı Arif Bey, who was his father's music teacher for qanun and the Hamoarsum notation of Ottoman classical music from Rauf Yekta. Later, he was able to dechipher the form called the "Mute Hamparsum notation". He received music lessons for about three years from Zekai Dede. He took lessons for viola d'amore and then for tanbur playing from Halim Efendi, Sheikh of the Rifa`i Order lodge in Kozyatağı. Among his music teachers are also Medeni Aziz Efendi, with him he performed fasıl during his time at the Military Medicine School, Hüseyin Fahreddin Dede, Sheikh of the Mevlevi Order lodge in Bahariye, Kadıköy, from him he obtained a rich repertoire of religious music, and Edgar Manas Efendi, from him he took lessons in western music and harmony after 1911. He composed more than 700 works in a great number of Turkish makams, however, he deemed only 165 of them worthy of publishing. His song Vatan Şarkısı, of which lyrics are written by poet Tevfik Fikret , was harmonized by Albert Lavignac, academic at the Conservatoire de Paris. 28 of his songs, which are compositions based on Ottoman poet Nedîm's odes, were included in the operetta Lale Devri by Musahibzade Celal in 1916. He also made some modifications in the Turkish music makams, and was music teacher, teaching the likes of Kemal Batanay, Ercüment Berker, Fahri Kopuz , Laika Karabey, Mesut Cemil, Yılmaz Öztuna, Ahmet Çağan and Arif Sami Toker. In 1932, he was appointed member of the Board for the Determination and Classification of Historical Turkish Music Works. at Istanbul City Conservatory. It began a period in which the research and study of Turkish music gained significance importance in his life. His board mission lasted 15 years. His research works, some of the in collaboration with others, were published by the Conservatory of Istanbul between 1933 and 1953. His works of Tanbur Metodu and Türk Musikisi Solfej Metodu were partly published in the Turkish Music Journal. In 1956, he published an article on the tempo in the Turkish Music in the Istanbul Institute Journal.