The 77-year-old was rushed to hospital early last month after suffering a stroke at this home in Prestwick. It was his third stroke this year.
He was later admitted to Ayrshire Hospice, where he died peacefully at 1.40pm yesterday.
The entertainer spent more than 50 years in the music industry alongside his brother Tom. The musicians took their classical training and began performing at local venues in and around their home in Cambusnethan, near Motherwell.
They went on to tour the globe on the back of hits such as Nobody's Child - which saw them outsell The Beatles in Scotland when it was released in 1964 - These Are My Mountains and the Northern Lights of Old Aberdeen.
In total, they recorded more than 30 albums and had their own TV series for many years. They were awarded MBEs in 2005 for their contribution to the entertainment industry.
The brothers were forced to retire last year due to Jack's failing health. Their farewell tour, before they hung up their accordions, was played to sell-out crowds at venues across South Lanarkshire.