Butch founded the business in Montego Bay in the early 1980s and grew it to its position now as one of the world’s foremost all-inclusive holiday brands.
Along the way, Butch was lauded for his efforts to champion the Caribbean and its potential as a tourist destination.
His death, aged 79, was announced on Tuesday (5 January).
Sandals’ UK boss Karl Thompson described Butch as a "true visionary", who was also akin to family to many at Sandals.
Stewart has been named chair of Sandals Resort International "in honour" of Butch’s long-term succession plans. He was appointed chief executive of the business in 2007.
"Our father was a singular personality," said Stewart. "An unstoppable force who delighted in defying the odds by exceeding expectations and whose passion for his family was matched only by the people and possibility of the Caribbean, for whom he was a fierce champion.
"Nothing, except maybe a great fishing day, could come before family to my dad. And while the world understood him to be a phenomenal businessman, which he was, his first and most important devotion was always to us. We will miss him terribly for ever."
Butch is survived by his wife Cheryl; his children Brian, Bobby, Adam, Jaime, Sabrina, Gordon and Kelly; his grandchildren Aston, Sloane, Camden, Penelope-Sky, Isla, Finley, Max, Ben, Zak, Sophie, Annie and Emma; and great grandchildren Jackson, Riley, Emmy and Willow.
A private funeral service will be held.
Anyone wishing to pay tribute to Butch, share memories, personal stories or photos, is asked to email AllThatsGood@sandals.com.
