The star was famous for his role as Mike Baldwin in the ITV soap.
A statement from his family said he died after a long illness.
"It is with great sadness that we announce the death of our father, Johnny Briggs," the statement said.
"He passed away peacefully this morning after a long illness, with family by his side. He was 85.
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"We politely ask for privacy at this time, so that we can quietly grieve as a family and remember the wonderful times we had with him."
The actor played the role on the Cobbles for decades.
His role as underwear factory boss Mike Baldwin was one of the soap's most famous.
Briggs made his Corrie debut as Mike in 1976 and remained on the cobbles until 2006.
He left the soap with his cockney character apparently suffering from a form of Alzheimer's.
The London-born actor also appeared on stage and in films, alongside the likes of Norman Wisdom, Dirk Bogarde and Tommy Steele.
Briggs was appointed an MBE in the Queen's New Year Honours in December 2006.
John Whiston, managing director of continuing drama and head of ITV in the north, paid tribute.
"The whole Coronation Street family is deeply saddened by the death of Johnny Briggs," he said in a statement. "For years Johnny was right at the centre of the show, playing the part of Mike Baldwin and bringing to the role huge energy, dynamism, professionalism and credibility.
"When Mike Baldwin was in a scene it was very hard to look at anyone else. And it was that charisma which made him irresistible to the women of Coronation Street, and to viewers.
"He truly was one of the most iconic characters the Street has ever known. We wish Johnny's family all our condolences."