Born in Pittsburgh, PA on June 30, 1923, Slepian's undergraduate studies at the University of Michigan were interrupted by service in the U.S. Army in World War II. Upon discharge, he entered Harvard University where he received a Ph.D. in Physics in 1949. After a postdoctoral fellowship at Cambridge University and the Sorbonne, he joined the Mathematics Research Center at Bell Telephone Laboratories. During the 1970's, Slepian shared time between Bell Labs and the University of Hawaii.

Slepian received many honors and recognitions, including: election to three national academies, the American Academy of Arts and Sciences, the National Academy of Engineering, and the National Academy of Sciences; the IEEE Centennial Medal in 1983; the SIAM von Neumann Award in 1982; the IEEE Alexander Graham Bell Medal in 1981; and the IEEE Information Theory Society Shannon Award in 1974. Slepian was the second Shannon lecturer, following Shannon himself.