Works on show at the Royal Pavilion include a painting of liger cubs given to King George IV, which will be on public display for the first time.
The cubs - a cross between a tiger and a lion - were born at Windsor in 1824.
The exhibition also tells the story of the first living giraffe in the UK, given to the king as a diplomatic gift.
The young female Nubian giraffe arrived in the UK in August 1827 after a long journey from Africa.
Two Egyptian cows were drafted in as wet nurses but she died less than two years later.
The Exotic Creatures exhibition in the Prince Regent Gallery runs until 28 February 2016.

The man, believed to be in his thirties, suffered neck injuries and was pronounced dead at the scene outside Southwark Park Primary School.
One witness tweeted he saw "a lot of blood" in the area after the accident at Banyard Road at around 11:00 GMT.
A Met Police spokesman said the incident had been referred to the Health and Safety Executive.
Another witness, Charlie Brenland said he saw police cordon off the road, adding: "Witnesses and the police said there had been an accident with a worker on one of the trees.
"Someone there said one of the tree surgeons had an accident with a chainsaw."
Emergency services, including a London Air Ambulance attended the scene shortly after 11:00 GMT but were unable to save the man.
A London Ambulance Service spokesperson said: "Sadly, despite the extensive efforts of our crews, a patient died at the scene."
The Metropolitan Police said next of kin had been informed.
A new exhibition in Brighton is exploring how animals considered exotic by the Georgians and early Victorians were depicted, kept and presented.
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A tree surgeon has died after reportedly injuring himself with a chainsaw in south London.