Tarmey, 71, appeared in the show for over 30 years from 1979 until 2010.
A family statement read: “The family of Bill Tarmey have confirmed that he sadly passed away this morning in Tenerife.
“They have respectfully asked the media for privacy as they grieve for a wonderful husband, father and brother.”
A statement from Corrie added: “The cast, crew and production team at Coronation Street are devastated to hear of Bill’s death.
“Our thoughts and prayers are with Bill’s wife and soulmate Ali and their family at this very sad time.”
The actor had previously suffered a minor heart attack following a bypass operation in 2002.
Tarmey is survived by his wife Alma and their two children, Carl and Sara.
It was rumoured only last month that Jack and Vera Duckworth (Liz Dawn) would return to reprise their well-loved roles in a spoof segment for Children in Need.
On filming his final scenes in 2010, Tarmey said: “It was delightful. And very moving. It was a case of, ‘Pass the hand towel’, never mind the box of tissues. I’ve become a right old Jessie in my old age.”
Tarmey revealed in an interview earlier this year that he left Coronation Street two years ago to care for his son Carl, who had suffered a brain tumour.