He was born at Pavlovsk, Imperial Russia, into a formerly sovereign family. His father, Prince Constantin Bagration-Mukhransky (1889–1915), a member of the Mukhrani branch of the Bagrationi family, formerly a royal dynasty of Georgia, was an Imperial Russian Army officer and was killed in World War I. Teymuraz"s mother, Princess Tatiana Constantinovna of Russia (1890–1979) was a member of the imperial Romanov dynasty of Russia.
Prince Bagration graduated in 1932 from the Krymskiy Cadet School and then studied at the Yugoslav Military Academy.
Teymuraz Bagration left Russia after the 1917 Revolution, first living in Switzerland and then settling in Yugoslavia. He served for ten years in the Guards Mounted Artillery Regiment of the Royal Yugoslav Army. During World World War II, he served in the Royal Yugoslav Army.
After the war, he emigrated to the United States. and was invited to join the Tolstoy Foundation in 1949.
He became Executive Director of the Foundation in 1979 and led the organization from 1986 until his death in New York in 1992.
Served at Lieutenant Royal Guard Artillery, Royal Yugoslav Army, 1935-1946, in charge missions with Royal Yugoslav Government, London, 1946-1949. Member Georgian Russian Eastern Orthodox Church.
Married Catherine Ratchich Bagration, 1940 (deceased 1946). Married Irina Czernichew-Besobrasow, November 27, 1949.
