Educated as an accountant, Telles worked at the United States Department of Justice for eight years. He was drafted into the Army in 1941. Telles then served in the U.S. Army Air Force where he became Chief of the Lend-Lease Program for Central and South America. Telles left the service with the rank of major.
Telles received the Peruvian Flying Cross, the Order of the Southern Cross from Brazil, the Mexican Legion of Merit and Columbian wings in recognition of the Lend-Lease Program. Telles served as aide to several Latin American and Mexican presidents visiting the United States, and as military aide to Presidents Harry S. Truman and Dwight D. Eisenhower when visiting Mexico City.
Telles was elected county clerk for El Paso County, Texas in 1948.
In 1951, Telles was recalled for the Korean Conflict. He served as Executive Officer of the 67th Tactical and Reconnaissance Group, U.S. Air Force. Telles was elected in 1957 mayor of El Paso and ran unopposed for a second term (1959-1961). He was appointed by President John F. Kennedy as Ambassador to Costa Rica. In 1967 President Lyndon B. Johnson appointed Telles chairman of the U.S.-Mexican Border Commission.