Entitled Royal Beasts, the exhibition will feature a series of specially-commissioned animal sculptures which will be installed around the Tower.
Animals, including lions, were housed at the Tower for many centuries before the responsibility for looking after them was passed to London Zoo in the 19th century.
Displays inside the Brick Tower and along the recently restored and opened north-wall walks will tell the story of the animals.
The royal zoo at the Tower was founded by King John who reigned from 1199 to 1216.
The first big cats were kept there in the 13th century, with Holy Roman Emperor Frederick II presenting England's King Henry III with three leopards after marrying his sister.
The earliest written record of an English lion occurs in 1240. It refers to the upkeep of "the King's lion".
In 1623 King James I was given an elephant by the King of Spain, with the beast's only drink being "a gallon of wine a day".
Ostriches were thought to have a huge appetite for iron. One of them died in the Tower after being fed more than 80 nails.
Skulls of dogs have been unearthed at the Tower. Dogs were often used to bait other animals such as lions, tigers and bears as part of spectator "sport".
Eventually, in 1834, the Tower's animals were transferred to London Zoo in Regent's Park.