David Lindsay Neill, 76, was the former captain of the Waverley paddle steamer and continued to deny the charges against him when he was jailed at the High Court in Glasgow in February, 2020.
The four charges of indecent assault were committed between March 1982 and September 1987.
An investigation will now be launched with a Fatal Accident Inquiry set to be undertaken.
The Scottish Prison Service said: “A prisoner from HMP Barlinnie has died.
"He was convicted at Glasgow High Court in 2020.
"Police Scotland have been advised and the matter reported to the Procurator Fiscal.
"A Fatal Accident Inquiry will be held in due course.”
Neill, from Galston, Ayrshire had previously been jailed for three years in 1998 at Glasgow Sheriff Court after being found guilty of abusing five teenage boys in his cabin between 1981 and 1987.