He was born in Boston, Massachusetts.
Elliott hosted "The Bob and Ray" show, from 1951 to 1953. The show starred Elliott and his long time sidekick Ray Goulding. Elliott appeared on a number of other television programs including "Happy Days", "Newhart" and "Bob & Ray, Jane, Laraine & Gilda" in 1979 (with Goudling, Jane Curtin, Laraine Newman and Gilda Radner).
In 1990, Elliott portrayed Fred Peterson in the Television series, "Get A Life", which starred his real life son Chris Elliott, who also played his son in the show.
In 1994, Elliott appeared in the Tim Burton produced film "Cabin Boy", where he played his real life sons father once again.