Selfridge, born in England, was a grandson of Harry Gordon Selfridge, the founder of Selfridges department stores. His father was Harry Gordon Selfridge Jr. and his mother was a clerk at Selfridge's store. His parents had met, fallen in love, married and had children all in secret, and Oliver never met his grandfather, Harry Sr. He was educated at Malvern College, and, upon moving to the U.S.A., at Middlesex School in Concord, Massachusetts, before earning an S.B. from MIT in mathematics in 1945. He then became a graduate student of Norbert Wiener's at MIT, but did not write up his doctoral research and never earned a Ph.D. While at MIT, he acted as one of the earlier reviewers for Wiener's Cybernetics book in 1949. He was also technically a supervisor of Marvin Minsky, and helped organize the first ever public meeting on artificial intelligence (AI) with Minsky in 1955.
Selfridge wrote important early papers on neural networks and pattern recognition and machine learning, and his "Pandemonium" paper (1959) is generally recognized as a classic in artificial intelligence. In it, Selfridge introduced the notion of "demons" that record events as they occur, recognize patterns in those events, and may trigger subsequent events according to patterns they recognize. Over time, this idea gave rise to aspect-oriented programming.
In 1968, in their formative paper "The Computer as a Communication Device", J. C. R. Licklider and Robert Taylor introduced a concept known as an OLIVER (Online Interactive Expediter and Responder), which was named in honor of Selfridge.
Selfridge spent his career at Lincoln Laboratory, MIT (where he was Associate Director of Project MAC), Bolt, Beranek and Newman, and GTE Laboratories where he became Chief Scientist. He served on the NSA Advisory Board for 20 years, chairing the Data Processing Panel. Selfridge retired in 1993.
In 2015, Duncan Campbell identified Selfridge as his "best source" for Campbell's 1980 reporting on US National Security Agency wiretapping activity at Menwith Hill, UK. Campbell described this operation in New Statesman as a "billion dollar phone tap".
Selfridge also authored four children's books: Sticks, Fingers Come In Fives, All About Mud, and Trouble With Dragons.
He was married three times, and had several children.