Tarmey played Jack Duckworth on the soap from 1979 to 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."
[Bill Tarmey with co-star Liz Dawn]
The actor had previously suffered a minor heart attack following a bypass operation in 2002.
Meanwhile, Tarmey's former Corrie co-star Julie Goodyear told Digital Spy: "This news is so very sad - not just for me but for all his other friends and of course for his wife Ali, and all his family. This wonderful man will be sadly missed."
Cast members Bill Roache (Ken Barlow) and Tarmey's on-screen son Nigel Pivaro have been among the first to pay their respects.
Tarmey is survived by his wife Alma and their two children, Carl and Sara.
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.
Jack Duckworth was named Coronation Street fans' favourite ever character in May this year.
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.
> Coronation Street Bill Tarmey dies: Reactions from soapland
> Bill Tarmey 1941-2012: Obituary for Coronation Street's Jack Duckworth
> Jack Duckworth's finest moments
Look back at Bill Tarmey's life and career in pictures below:
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