Mr Oliver claimed the young lions would have faced being put down if he lost the appeal, but despite planning officers advising refusal, councillors backed it, citing limited visual impact and lack of alternate homes for the animals.
Chairman of the council’s planning committee, Councillor David Watts, said: “In total I’ve sat on the planning committee for sixteen years, most of that as chair.
“This is by far the most unusual application that we have dealt with in that time.
“I’ve been talking to Lib Dem colleagues up and down the country and I haven’t come across anyone who has had an application like this before.”
Speaking after the meeting on Wednesday evening, Mr Oliver told the BBC that his heart had been going “at a million miles an hour”, and he had thought he would lose the animals.
“It’s the best feeling in the world, it’s the best result ever,” he said.
“I love those animals, they’re like children to me. It would have been like taking my children off me.”
Mr Oliver also came to national attention in January after he bought two penguins online that turned out to be stolen.