During World War II, as part of the Armed Forces Radio Service (AFRS), he entertained troops in the Pacific with his program of comedy and music, where he created the character of Tokyo Mose, a lampoon of Japan’s Tokyo Rose.

After his discharge, Averback’s big break came when he was hired to announce the Jack Paar radio show, which replaced Jack Benny for the summer of 1947. From there, he became the announcer for Bob Hope on NBC in September 1948, and announced NBC radio shows The Sealtest Village Store and Let’s Talk Hollywood. He announced the Sweeney and March show on CBS in 1948, and became the voice of Newsweek‘s weekly radio magazine show on ABC’s West Coast stations.

Averback was also an actor, appearing a number of times on the Jack Benny radio show, beginning in January 1948.

In 1952, Averback starred in Secret Mission, a transcribed program “dealing with factual stories of escape from behind the Iron Curtain” on AFRS. In 1955 he joined the ensemble cast of Yours Truly, Johnny Dollar, playing multiple character roles in support of leading actor Bob Bailey.

Doing comedy on early television, he appeared on The Saturday Night Revue (1953–54), Tonight (1955) & NBC Comedy Hour (1956). He was a series regular as Mr. Romero on the Eve Arden sitcom Our Miss Brooks & appeared on I Love Lucy & other 1950s comedies, then moved into directing at the end of the decade. He directed The Real McCoys with Richard Crenna. Crenna had been a cast member with Averback on Our Miss Brooks.

Averback also directed for The Dick Powell Show (1961–1963), Burke’s Law (1963-1964), The Man from U.N.C.L.E. (1964–1968), The Flying Nun (1967–1970), Columbo: Suitable for Framing (1971), McCloud (1971), McMillan & Wife (The Face of Murder, 1972), M*A*S*H (1972), Needles and Pins (1973), Quark (1977–1978), the miniseries Pearl (1978), Matt Houston (1982–1983), The Four Seasons (1984), Murder, She Wrote (1985), & The Last Precinct (1986). For CBS, he produced Mrs. G. Goes to College (aka The Gertrude Berg Show) in the 1961–1962 season.

He co-produced the popular 1960s sitcom F Troop and supplied the voice over the loudspeaker heard on the television series M*A*S*H. His actual recording from a Bob Hope show was used in M*A*S*H episode 63, “Bombed,” from season 3 where he announces himself as Hope’s announcer.