Born in New Haven, Connecticut, Elgart grew up in Pompton Lakes, New Jersey with his brother Larry. They were exposed to musical influences early in their lives. Their mother, Bessie (Aisman) Elgart, was a concert pianist before her marriage to Arthur Elgart, a manufacturer's representative. She is said to have given a piano recital at Carnegie Hall, and at one time had her own music conservatory. At age 10, Les was attracted to bugling after joining the Cub Scouts. Later, he turned to the cornet, and then the trumpet. Both brothers attended Pompton Lakes High School, where Les was elected president of the school orchestra. He was playing professionally by the age of twenty.

In late 1952, Larry Elgart was working with fellow saxophonist Charles Albertine in the pit band for the Broadway play "Top Banana". Larry said, "We wondered if this was it... if this was what we had to do to make a living in the music business. But we knew it wasn’t. And that’s why Les, I and Charlie started a new band with the determination that it had to happen.

With $1,000, they gathered sidemen and recorded three demo tracks to shop the record labels. In April 1953, Columbia Records A&R executive George Avakian liked what he heard, and signed the band to the label. "Sophisticated Swing," the band’s first album, was released that year. It enjoyed immediate success. The Elgart ensemble was lauded as "a new band with a handsome sound and smart arrangements." The band came from nowhere to third place in the 1954 DownBeat Magazine popularity poll, behind the Les Brown Band and the Ray Anthony Orchestra. Elgart displaced Anthony for second place in 1955 and again in 1956.

Over the next three years, the band released a half dozen albums and enjoyed success on tour, with many appearances on college campuses. The band's unique blend of brass and reeds became known as “The Elgart Sound." The best selling albums were "The Elgart Touch" (1956) and "For Dancers Also" (1957), both of which reached the Top 15 on the LP charts. Among the band's popular tunes was "Bandstand Boogie", which was used by Dick Clark as the theme song for the ABC-TV dance show American Bandstand.

The band's first stereo recording in 1957 reflected a name change to Les and Larry Elgart and Their Orchestra. After the 1958 release of “Sound Ideas," however, the brothers parted ways, and Larry formed his own band.

The popularity of the Les Elgart Orchestra remained strong. The band took second place, again behind Les Brown, in the 1959 DownBeat poll. In 1960, the band won the Cashbox Magazine award as the Most Programmed Band by America's Disc Jockeys, and the Billboard Magazine award as "America’s Favorite Band 1960 Outstanding Achievement in Recorded Music."

By the end of the decade, Les quit performing, preferring to handle the business aspects of the band. Under several producers and arrangers, the band released eight more albums.

The brothers reunited again in 1963, hiring arrangers Charles Albertine and Bobby Scott. The Les and Larry Elgart Orchestra attempted to align itself with popular music trends such as folk ("Big Band Hootenanny" 1963) and disco ("Elgart Au Go-Go" 1965). Its remaining releases, arrangements of contemporary hits, could be categorized as easy listening. The band performed on the radio between 1964 and 1966, and appeared on a Jackie Gleason television special featuring big bands in November 1966. Veteran Columbia Records producer Teo Macero produced the Elgarts' final three albums for the label. After 1967's The Wonderful World of Today’s Hits, Les and Larry parted again, this time for good.

In 1969, Larry was invited to London to make three records for Swampfire Records under the imprint of Les and Larry Elgart. The albums claimed a Nashville sound and bore no relationship to the Elgart Sound of the early 1950s.

Les Elgart lived in Chicago for several years, and Santa Monica and Hollywood Hills on the West Coast. He returned to Chicago, then relocated to Miami, and San Antonio, Texas. From his home in Dallas, Les continued to tour with his band, performing at colleges and conventions, and on cruises. In 1977 he married Joerene Ingram, who managed the band. In 1987 Les Elgart traveled to Brazil at the invitation of Brazilian radio program producer and Elgart biographer Joaquim Gaspar Machado.

Les continued to work until his death from heart failure, in Dallas, Texas, at age 77.