Stewart said his father, who was born in Kingston, Jamaica, "lived a big life" and was a "fierce champion" of the Caribbean and its tourism industry.
Butch is credited with popularising the all-inclusive resort experience throughout the Caribbean, building Sandals to a market leader.
According to Stewart, in a statement provided to the Jamaica Observer, his father opted to keep "a very recent health diagnosis" private.
He described him as a gifted entrepreneur, marketing genius and talented showman – a dreamer "who could dream bigger and better than anyone".