Drake, who was born in Chicago, Illinois, graduated in 1952 from Cornell University and obtained his PhD in 1958 from Harvard. He worked initially at the National Radio Astronomy Observatory (NRAO), West Virginia (1958–63) and at the Jet Propulsion Laboratory, California (1963–64) before returning to Cornell and serving as professor of astronomy from 1964. He was appointed professor of astronomy at the University of California in 1984.

Although Drake has made significant contributions to radio astronomy, including radio studies of the planets, he is perhaps best known for his pioneering search for extraterrestrial intelligence. In April 1959 he managed to gain approval from the director at NRAO, Otto Struve, to proceed with his search, which was called ‘Project Ozma’. The name was taken from the Oz stories of Frank Baum. Drake began in 1960, using the NRAO 26-meter radio telescope to listen for possible signals from planets of the Sunlike stars Tau Ceti and Epsilon Eridani, both about 11 light-years away. He decided to tune to the frequency of 1420 megahertz at which radio emission from hydrogen occurs. This would have considerable significance for any civilization capable of building radio transmitters.

No signals were received although at one time excitement was generated when signals from a secret military radar establishment were received while the antenna was pointed at Epsilon Eridani. In July 1960 the project was terminated to allow the telescope to fulfill some of its other obligations. Drake revived the project in 1975, in collaboration with Carl Sagan, when they began using the Arecibo 1000-foot (305-meter) radio telescope to listen to several nearby galaxies on frequencies of 1420, 1653, and 2380 megahertz. No contact was made nor was it likely, they declared, for “A search of hundreds of thousands of stars in the hope of detecting one message would require remarkable dedication and would probably take several decades.” He has published a number of works on this issue including Is Anyone There? The Search for Extra Terrestrial Intelligence (1992).