The new series, Jack Osbourne's Buried Bloodlines, is presented by the TV personality on Discovery+ and features appearances from his mother Sharon Osbourne and medium Hayley Lily.
In Tasmania, Osbourne learns about his family ties to the area as he explores the Willow Court Asylum and Hobart, including the city's convict prisoners' barracks, Hobart Convict Penitentiary, known as the Tench.
The 37-year-old said: "There were probably two or three times I was really freaked out during filming this series.
"The first was probably the Tench, being around the gallows, this is the only original gallows left in the country of Australia.
"They've had to refurbish it and whatever, but it's pretty much all the same. When we went to the asylum we heard some wild noises, there was... it was crazy, I don't want to give it away but it was pretty cool."
Osbourne also said he was "probably the worst person in the world at preparing for a ghost hunt", having starred in other similar shows, Jack Osbourne's Haunted Homecoming and Portals To Hell.
He said: "I'll obviously read the write-up, but I don't like to do too much, just because I find it can sway you, you make your mind up about a place.
"Let's be honest, any time you go and investigate a place for the paranormal there's always the tell-tale stories, people say 'Oh, they're shadow figures', 'We hear disembodied voices' or 'We've seen an apparition.'
"There's only a handful of things that really happened with ghost hunts, and so you kind of go in there expecting all of the above.
"The stuff that really perks my attention is when you read about something or you hear about something that is totally new and different.
"For instance, investigating the Tench... I've never investigated something where the original gallows are still in place. That was pretty cool. So, learning about that kind of stuff is what I tend to do. "
He said he would next like to investigate Australia, New Zealand or South East Asia.
"There are some phenomenal mediums around Malaysia and things like that, that do some really interesting work," Osbourne added.
"I'd like to do something like that, a bit more adventure."
He rose to fame when he starred alongside his parents, Sharon and Ozzy Osbourne, in the family's own MTV reality show.
The presenter has also worked on the BBC's Saving Planet Earth and History's Ozzy & Jack's World Detour.
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