The New Orleans native died April 14 at Brotman Medical Center, The Los Angeles Times reported.
Besides Basie, Riley played with Jimmy Smith, Bobby Bryant and Lavay Smith, among others. His one album as a band leader, "Herman," came out in 1984.
"There are some musicians ... who certainly shine as soloists out front," said George Bohanon, a musician who was a longtime friend of Riley's. "But when you have to support someone -- not get in their way but enhance what they're doing -- that's a special talent. He's the greatest at that. He'd play one or two notes and you'd beg him to play another."
Riley is survived by his wife Thelma, daughter Shenell Riley Boone, a grandson and two brothers. He was preceded in death by his son, Patrick.