Mr Mallan's family confirmed he had passed away "suddenly but peacefully" at the Victoria Infirmary in Glasgow on Friday.
He was raised in the Gorbals area of Glasgow and left school at 15, later becoming a firefighter with Glasgow Fire Brigade at the age of 21.
He was among those on duty on the night of the Cheapside fire disaster in 1960, when 19 firefighters lost their lives responding to a blaze at a whisky depot in Glasgow's Cheapside Street.
In later life, he became an honorary member of Strathclyde Fire Brigade.
However, it was as a singer and broadcaster that he became a household name.
He first appeared on television on BBC's "Children's Hour," going on to appear in "Jigtime;" "The One O'clock Gang," and; "The White Heather Club."
He would also become principal teacher of music of Scotland's largest comprehensive school, Holyrood Secondary in Glasgow.
Mr Mallan is survived by his wife Helen, their son John, their son-in-law Lindsay (who was married to the couple's late daughter, Jennie) and by grandchildren Heather and Thomas.
A funeral service for Mr Mallan will be held at Linn Crematorium in Glasgow on Friday at 3pm.