Rayburn was born Eugene Rubessa in Christopher, Illinois (he chose his stage name by randomly pointing at a page in the phone book after being told Rubessa sounded 'too Italian'). He was the only child of Croatian immigrants, and he graduated from Knox College. After the birth of his first child Lynn, Rayburn was quickly drafted into the U.S. Air Force. Rayburn became a popular radio personality in New York City on WNEW-AM. He was half of the first two-man team in morning radio, partnering with Jack Lescoulie and later Dee Finch. before breaking into television as the original announcer on The Tonight Show in 1954. He hosted his first game show, Make the Connection, in 1955; from there he hosted shows such as Choose Up Sides, Dough Re Mi, and Tic Tac Dough. On radio, Rayburn become one of the many hosts of the popular NBC program Monitor in 1961 and remained with the show until 1973.

In 1962 Rayburn first hosted the game show that he was best known for hosting, The Match Game. The original version, which aired on NBC, lasted until 1969; in 1973 the show returned to CBS with a new format in which contestants must match celebrity answers to humorous fill-in-the-blank questions. Millions tuned in and soon the show became the highest-rated daytime TV show. From 1973 to 1977, it was #1 among all game shows, fueled mostly by the zany questions and Rayburn's witty emceeing style which captivated audiences. His interaction with the panel and contestants and his many antics during the show's run--including breaking through the entrance doors, roller-skating on stage, climbing the audience, and much more--all made the game show a classic. The popular daytime revival of Match Game, which featured regular celebrity panelists Richard Dawson, Brett Somers and Charles Nelson Reilly, ran until 1979 with a concurrent 'nighttime version, Match Game PM, airing from 1975 to 1981. Rayburn was nominated for two Daytime Emmy Awards for Outstanding Host or Hostess in a Game or Audience Participation Show for his work on Match Game. In 1983 the show was revived as part of the Match Game-Hollywood Squares Hour, with Rayburn hosting the Match Game segment and sitting on the panel of the Hollywood Squares segment. The show lasted only nine months on NBC. In a 1996 interview, Rayburn said that hosting the MG-HS Hour was "as boring as hell."

During and between his Match Game years, Rayburn also served as guest panelist on two other Goodson-Todman shows, What's My Line? and To Tell the Truth, where he exhibited the same inquisitiveness on serious subjects he showed on Monitor. Three years after the 60s Match Game was cancelled, Rayburn hosted a short-lived Heatter-Quigley Productions show called The Amatuer's Guide to Love, which aired in 1972. Rayburn also hosted a pilot for Reg Grundy Productions in 1983 called Party Line, which would make TV three years later as Bruce Forsyth's Hot Streak (and be cancelled after 13 weeks).

The final game shows Rayburn emceed were: a 1985 revival of Break the Bank which bombed in the ratings (and from which Rayburn was fired after 13 weeks and replaced by Joe Farago) and The Movie Masters, an AMC cable game show Rayburn seemed to enjoy more, that ran from 1989 to 1990.

Right before production was to begin on a new Rayburn-emceed "MG" revival in 1985, a Entertainment Tonight reporter publicly disclosed his age, which was much older than many people believed. Rayburn had trouble finding jobs after that, blaming the reporter for disclosing his age and subjecting him to age discrimination.

Rayburn died in late 1999 at his daughter's home in Gloucester, Massachusetts, of congestive heart failure at the age of 81.