Morrow, whose career spanned more than 75 years, died Sept. 27 at his longtime home in Maitland, Fla., his family said.
After two weeks, "I realized that this was what I wanted to do," Morrow told the Arkansas Democrat-Gazette in 1995. "So I called the agent and said, 'Don't look for anyone else, I'm keeping it!' "
He last appeared with the orchestra Sept. 24 in Ormond Beach, Fla. Although he needed to be helped onstage, he played his classic trombone solo on "Night Train," a catchy R&B-influenced interpretation of the song that was a hit for him in 1952.
In the late 1930s, swing-era bandleader Bunny Berigan heard a teenage Morrow sitting in on a jam session in New York and persuaded him to join the Artie Shaw Orchestra.
Morrow went on to play in the Tommy Dorsey Orchestra in 1938 and was featured in bands led by Eddy Duchin, Paul Whiteman and others.
In 1950, Morrow formed his own orchestra, which often had success by giving an R&B twist to older standards. The band's hits included "One Mint Julep" and "Hey Mrs. Jones."
Morrow was born Muni Zudekoff on Feb. 8, 1919, in New Haven, Conn., to immigrants from Poland and Russia. The fifth of six children in a musical family, he ended up learning trombone at age 12 because an older brother had already claimed the trumpet.
Within a year, Morrow was performing in local dance bands, and by 15 he was playing at college dances and parties with the Yale Collegians.
After moving to New York City, he accompanied a roommate to an audition at the Juilliard School and was mistakenly asked to try out. Caught unprepared, he played from memory difficult passages from "Arban's Famous Method for Trombone," considered a bible of sorts for trombone players, said Terry Myers, a friend and musician.
Juilliard offered him a full scholarship when he was 16, and he attended the school for a year before he was recruited for the Artie Shaw Orchestra.
In the early 1940s, he served in the U.S. Navy musicians unit and adopted the name Buddy Morrow.
"I was stateside during World War II, working as a 'morale booster,' they called us," he told the Democrat-Gazette. "We did dances practically every night."
After the war, he joined the Jimmy Dorsey Band — run by Tommy Dorsey's brother — and filled in for the conductor when he fell ill.
In the 1960s, Morrow regularly performed with NBC's "The Tonight Show" and was a studio musician for much of the 1960s and 1970s.
Of the big-band music that long dominated his life, Morrow told the Elmira, N.Y., Star-Gazette in 2001: "It's still very much a part of Americana and what we export to the world. It was developed here, and it will be here long after you and I are gone."
Morrow is survived by Carol, his wife of 40 years; two daughters, Sara Morrow of Los Angeles and Catherine Morrow-Miller of Atlanta; a son, Peter Morrow, of Hillsdale, N.J.; and three grandchildren.