The television presenter and chef died suddenly in Melbourne on Sunday.
The Zonfrillo family described him as an irreplaceable husband, father, brother, son and friend.
"With completely shattered hearts and without knowing how we can possibly move through life without him, we are devastated to share that Jock passed away yesterday," the family said in a statement.
"So many words can describe him, so many stories can be told, but at this time we're too overwhelmed to put them into words.
"For those who crossed his path, became his mate, or were lucky enough to be his family, keep this proud Scot in your hearts when you have your next whisky."
Broadcaster Network 10 and production company Endemol Shine Australia said they were deeply shocked and saddened.
"Jock's charisma, wicked sense of humour, generosity, passion and love for food and his family cannot be measured. He will be greatly missed," they said.
He opened Adelaide restaurant Orana in 2013 after working in top kitchens around the world including Marco Pierre White's acclaimed restaurant in London.
He joined MasterChef Australia in 2019.
The program will not air this week.
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