Barcelona, who died April 1, traveled around the globe with the jazz great and played on scores of recordings, including Armstrong's signature hit, "Hello, Dolly!," the Los Angeles Times said.
Born in Hawaii, the self-taught drummer joined Armstrong's All Stars in 1958.
"Danny was excellent," Buddy Catlett, who joined the Armstrong band as bass player in 1965, told the Times. "He was a good show drummer on top of it. Louis kept a sense of showmanship going at all times, and Danny did his part."
After Armstrong died in 1971 and the band broke up, Barcelona played with the Bernie Hallman Group at the Hilton Hawaiian Village in Honolulu. He later worked at Harry's Music in Kaimuki, which supplied instruments to the local school district, and taught drums before moving to Monterey Park, Calif., in 1979.
Barcelona is survived by his wife, Dee; daughters, Dana Barcelona-Bonner and Jodi Barcelona; his brother, Jose "Sonny" Barcelona; five grandchildren and a great-grandson.