The band's management told the BBC that Shelley died on Thursday 6 December in Estonia where he was living.
Shelley, whose real name was Peter Campbell McNeish, was inspired to form Buzzcocks after seeing the Sex Pistols perform, according to Variety.
It did not elaborate on the details of Shelley's death but said that more information would be released later.
The Buzzcocks formed in the mid-70s, and became known for their catchy songwriting as well as their business saavy, forming their own label, New Hormones, when independent artists were still an anomaly.
They debuted a year later, opening for the Sex Pistols. Devoto soon left the group, leaving Shelley to handle songwriting and vocal duties on top of his work as guitarist. It was in support of 40th anniversary reissuses of their seminal first two albums, Another Music In Different Kitchen and Love Bites.
The band were part of the British punk/new wave eras with singles such as Orgasm Addict, What Do I Get?, and Ever Fallen in Love (With Someone You Shouldn't've). Following the band's breakup, Shelley released a string of solo albums, including 1981's Homosapien and 1983's XL1.
Buzzcocks emerged from the late-1970s punk scene in the United Kingdom alongside contemporaries the Sex Pistols.