He began working in radio in 1922 as a pianist on KYW (Chicago) and moved on to CBS, where he created music for such radio shows as The Whistler, Suspense, Meet Corliss Archer, My Favorite Husband, Broadway Is My Beat, Our Miss Brooks and The Screen Guild Theater.
Hatch also worked as a conductor and music director for CBS. During the late 1930s and early 1940s he was conductor on The Campbell Soup Radio Show. He was the musical director and composed the theme for CBS Radio's The Whistler (1942–55). Additionally, he was the musical director for CBS Radio's Broadway Is My Beat (1949–54) and Luke Slaughter of Tombstone (1958).
His most lasting on-screen television credit was for composing some of the music and conducting the Desi Arnaz Orchestra on I Love Lucy. (In Episode #44, as Ricky is about to sing, he calls offstage "Mr. Hatch, if you please.") He was the sole composer for three episodes of I Love Lucy (1951–56), four episodes of The Lucy-Desi Comedy Hour (1959–60), all 156 episodes of The Lucy Show (1964–67) and all of the Here's Lucy (1968–69) episodes up to the time of his death. He also conceived and conducted the music for the TV versions of Our Miss Brooks and December Bride, as well as its spin-off, Pete and Gladys. He also composed music for The Mothers-in-Law. Until the time of his death Hatch was resident musical director of Desilu Studios, and his work included music director on Star Trek, The Untouchables, and other Desilu productions. In 1970, after Hatch had died, Marl Young (1917–2009) became the resident music composer for Lucille Ball Productions, Inc. (including the Here's Lucy series until it finished in 1974).
Hatch attended the University of Chicago to study engineering, but music fully occupied his life. One of the highlights of his college education was that he wrote the music for the annual Blackfriar's show, the University's dramatic organization. Wilbur graduated from University of Chicago with High Honors and a Phi Beta Kappa Key.
Wilbur was married to Margaret Mathews of Grinell, Iowa. They had three children together: Robert Allen (born in 1932), Nancy Margaret (born in 1934) and Margaret Ann (born in 1944).
He is buried at Mountain View Cemetery, Altadena, Los Angeles County, California.