Ambaye was born in Keren in 1906. At an early age, he joined the Catholic seminary where his grandfather had taken shelter when he moved to Keren. Due to his outstanding academic achievement at seminary, he was selected to attend the Vatican College. He later studied law at the University of Paris, France. In the late 1920s and early 1930s Crown Prince Haile Selassie toured Europe and made diplomatic contacts with European governments. While touring he also wisely expanded his network by meeting educated Eritreans and Ethiopians. During one of these trips, Crown Prince Haile Selassie had a prudent meeting at the Vatican with Ambaye, who was ready to be ordained as a Catholic priest. At a crucial moment in Ethiopia's history, the Crown Prince noticed Ambaye's potential and recruited him to help build a modern government. Realizing the opportunity to struggle for the liberation of Eritrea from Italian colonialism, Ambaye joined the Imperial Government of Ethiopia. The Emperor awarded him a scholarship for further higher education at the University of Paris Law School. In 1935, during the Italian occupation of Ethiopia, Dr. Ambaye joined the Emperor into exile, first to Djibouti and then to Cairo via Khartoum. On behalf of the exiled Ethiopian government, he participated in anti-fascist political activities. He represented the Emperor, acting as both a decision maker and political activist in the Middle East. His expertise spanned across contacts in Tokyo, Japan; in 1936, he served for one year as the emperor's unofficial diplomatic emissary to the Imperial Government of Japan. After the defeat of the fascists, he returned to Ethiopia. He participated in modernizing the judicial system of Ethiopia. He worked closely with Blatengeta Lorenzo Taezaz in international judicial matters. He was a signatory for the establishment of the International Court of Justice in The Hague, Holland. In 1946, he was assigned to present Ethiopia's claim to try fascist war criminals, to the UN War Crimes Commission. He was a member of the Anglo-Ethiopian Boundary Commission in 1947. In 1945 Dr. Ambaye Wolde Mariam, Ato Aklilu Habte-Wold and Blatta Ephrem Tewoldemedhen represented Ethiopia as delegates and signatories on various committees for the establishment of the United Nations. Dr. Ambaye had many disagreements with the powerful Imperial Palace Authorities, of the time. One of the major disagreements was over the prospect of the division of Eritrea. The British and the Palace Authorities entertained to divide Eritrea between Sudan and Ethiopia. Dr. Ambaye, whose family origin embraces the highlands and the lowlands of Eritrea, was adamantly opposed to the idea of splitting the nation of Eritrea. He was very proud of his cultural patrimony. He attempted to resign from the government several times over this issue. It was his friend and next door neighbor, Ato Aklilu Habte-Wolde that persuaded him to stay the course In the early fifties, Dr. Ambaye started getting ill. In 1953 when he was an Acting Foreign Minister, he suddenly became gravely ill. He died at the age of 46. The Imperial government had earlier sent him to Sweden for medical treatment.
