Harris, who played on the No. 1 instrumental hit "Apache," was 71, the BBC reported.
He died Friday at the home of partner Janet Hemingway, who was listed as his survivor.
"Jet was exactly what The Shadows and I needed -- a backbone holding our sound together," said former band mate Cliff Richard. "Jet will always be an integral part of British rock 'n' roll history."
Agent Peter Stockton said Harris was confident he would beat the disease, but he canceled all his appearances in early March because of poor health.
"He was a man who was so courageous and determined and kept saying 'I will beat this,'" Stockton said. "The last time he went on stage he said he didn't want to let people down ... he got a standing ovation. Regrettably it was the last concert he did on February 5."
The bassist was born Terence Harris in London on July 6, 1939.
He joined the Most Brothers on tour in 1958. Cliff Richard and the Drifters were on the same bill. He later joined the group and is credited with coming up with its new name, The Shadows.
He left The Shadows in 1962.
Harris was awarded a Fender Lifetime Achievement Award for his role in popularizing the bass guitar in Britain in 1998.
He released a new album, "The Journey," in 2007 and continued to tour in England with the Shadows tribute band, The Rapiers.