Elliott was born in Winchester, Massachusetts, the son of Gail Marguarite (née Brackett), a needleworker, and Fred Russell Elliott, who worked in insurance. Bob Elliot served In the U.S. Army in Northern Europe in WWII. On radio, he appeared in programs with his long-time partner Ray Goulding. These were in different series and time slots over decades, beginning in the late 1940s at Boston's WHDH radio when the two were first paired for Matinee with Bob and Ray. The team’s ersatz advertisements included exhortations on behalf of the Monongahela Metal Foundry (“Steel ingots cast with the housewife in mind”), Einbinder Flypaper (“The flypaper you’ve gradually grown to trust over the course of three generations”) and Height Watchers International.