A statement from Ayrshire Hospice said he died peacefully at 1.40pm today with his family around him.
In October he was rushed to Ayr Hospital from his home in Prestwick after suffering a massive stroke.
Jack and Tom, originally from Cambusnethan in Wishaw, Lanarkshire, were among Scotland's best loved entertainers before they quit in 2012 after 54 years in showbusiness.
They recorded more than 30 albums and toured Canada, the United States, Australia and New Zealand and outsold The Beatles in Scotland with 1964 hit single Nobody’s Child.
They had their own TV series for many years and appeared on the legendary Sunday Night at the Palladium, even co-starring with Shirley Bassey.
They were made MBEs for services to entertainment in 2005.
Their farewell tour before hanging up their accordions was in south Lanarkshire, where they played to sell-out crowds.