Hooper was born in Colton, California, and educated in the San Bernardino public schools. At age 8 his father built him a telegraph transmitter and taught him Morse code; by age 10 he was working as a relief telegraph operator during summer vacations. He entered the United States Naval Academy at age 15, and after graduation in 1905 served on various ships. From 1910-1911 he taught electricity, physics, and chemistry at the Naval Academy, then from 1912-1914 (and again 1923-1925) served as the first Fleet Radio Officer, where he created the Navy's tactical signaling codes. From 1914-1928 he was in charge of the Navy's Radio Division, in which role he commanded the USS Fairfax (DD-93) in World War I, for which he was awarded the Navy Cross for distinguished service, and also in 1922 supervised installation of the first wireless telephone in the White House for President Warren Harding. Afterwards he served as Director of Naval Communications until 1945, then held offices with commercial electronics firms until his death.
Hooper conducted pioneering radio tests, established land stations for communication with the fleet, and served as technical advisor and head of many boards and committees dealing with communications. Hooper received the IEEE Medal of Honor in 1934 "for the orderly planning and systematic organization of radio communication in the Government Service with which he is associated, and the concomitant and resulting advances in the development of radio equipment and procedure." In 1945 he received the Eliot Cresson Medal for research in radio electronics from the Franklin Institute of Philadelphia, and in 1948 an honorary LL.D. from Drury College. He also received the French Légion d'honneur, the Department of Navy Electronics Trophy, and the Marconi Medal of Honor. The USS Hooper (DE-1026) was named in his honor, and he is honored annually via the Rear Admiral S. C. Hooper Trophy.