He was the son of Henri Ely, a civil servant and Therese (née Coste). He attended the Lycée de Best.
Ely attended the Ecole Spéciale Militaire de Saint-Cyr and was commissioned as a lieutenant in 1919. He was promoted to captain in 1930 and then commandant in 1938. He was promoted to lieutenant colonel in the Free French forces in 1942 and full colonel in 1944. In 1946 he was promoted to general. 
Ely was appointed as the first Chief of the Defence Staff and served in this role from August 1953 to June 1954, March 1956 to May 1958 and from June 1958 until February 1959. Ely retired from the Army in 1961.
Ely died on January 16, 1975.