In 1918, Ziggy's family moved to Atlantic City, NJ, and that's where Elman was educated. While still a teenager, Ziggy, working mostly as a trombonist, joined the Alex Bartha Orchestra which was then based at Atlantic City's famed 'Steel Pier'.

In 1935, Benny Goodman chose him to replace Pee Wee Erwin, and he remained with Benny until the summer of 1940. It was with Goodman that Ziggy had his first and biggest success. Ziggy's talent, youthful exuberance and brashness came to the fore when Benny allowed him to interpolate Yiddish "Fralich-er" (Yiddish for 'happy-like') phraseology into his solos. The public simply adored this. Probably the best known example of Ziggy's style is Benny's recording of "And The Angels Sing" - as popular today as when it was first 'laid down on wax'.

While with Goodman he recorded 20 sides for the Bluebird label. Although the labels indicate "Ziggy Elman and His Orchestra" these records actually have Elman leading a band made up of members of Goodman's orchestra.

After leaving Goodman he spent a month with Joe Venuti before joining Tommy Dorsey, in 1943, as Bunny Berigan's replacement. He remained with Dorsey until called into the Army in 1944. He led a band while in the service and after being discharged rejoined Dorsey in February 1946 and stayed until the band broke up in 1947.

Ziggy then took up residence in Los Angeles, CA, where the Palladium Ballroom engaged his services. He organized his own band and negotiated his own record contact. This band lasted only a few months and when Dorsey started a new band (July 1947) Elman signed up. He stayed with TD for about a year before leaving to form his second band. He disbanded in 1951 and spent the rest of his career doing studio work and club dates mainly on the west coast. Former Goodman vocalist Louise Tobin recorded with him on a studio session in 1951.