His family announced he died Feb. 25 in the city he has called home since 1998, The New York Times reported Thursday.
Tsegaye wrote more than 30 plays -- his first at age 13 -- and translated many other works, including those by Shakespeare, Brecht and Moliere, into Amharic, which is Ethiopia's official language, the Times said.
He also published countless poems and was an expert in the history of his native land.
He graduated from Chicago's Blackstone School of Law in 1959 and went to Europe less than a year later to study theater.
He returned to Ethiopia and was artistic director of the Ethiopian National Theater from 1961-71 he founded the department of theater at Addis Ababa University. He was arrested and held without charges after a military junta in the 1980s and saw many of his works banned.
Tsegaye left Ethiopia for New York in 1998 to receive treatment for kidney disease.
He is survived by his wife, three daughters and three sons.
He has been buried in the same national cathedral in Addis Ababa as the final Ethiopian monarch, Emperor Haile Selassie.