Shelley formed the group in 1976 and they achieved commercial success with hits including Ever Fallen In Love (With Someone You Shouldn't've).
He wrote: "This is the hardest thing I have ever had to do, is tell you my brother Pete Shelley had a heart attack this morning and passed away". BBC reported the musician's death after being informed by the band's management that Shelley died Thursday in Estonia, where he was living at the time.
In prior interviews, the band said they thought the use of the name would only last for one pilot or just a few episodes, but the show ended up running for years.
Buzzcocks released three albums, Another Music in a Different Kitchen (1978), Love Bites (1978) and A Different Kind of Tension (1979) before their initial break-up in 1981. Impressed by the Sex Pistols' high-energy performances, they brought the band to Manchester.
World's first baby born using transplanted uterus from deceased donor
The recipient was given drugs that weakened her immune system to prevent her body from attacking and rejecting the transplant. The current norm for receiving a womb transplant is that the organ would come from a live family member willing to donate it.
Buzzcocks most recently released music in 2014 with their ninth studio record The Way.
After the band split, Shelley released his own music, with his debut single Homosapien being banned by the BBC for "explicit reference to gay sex".
Shelley's solo career then spawned 1983's XL1 and 1986's Heaven and the Sea before Buzzcocks reformed in 1989.
Shelley became the primary songwriter for the Buzzcocks in 1977, following the departure of original lead singer Howard Devoto.