The zoo said it was a huge event for them and the birth of four healthy cubs is very rare - usually a white Bengal tiger will have only two.
Three of the newborns are boys and one is a girl.
Currently, there are only a few hundred of the endangered white tigers left in the world, including the cubs' mother Tigryulya who was a gift to the zoo in 2009 by former Ukrainian Prime Minister Yulia Tymenshenko.
The gift followed a month of suspicious animal deaths at the zoo. It is thought they were poisoned but those responsible were never found.
White tigers are extremely distinctive due to their pale colouring - lacking the red and yellow pigments that produce the orange colour of other tiger subspecies. They also tend to be somewhat bigger than other tigers.
Over the last 100 years, hunting and forest destruction have reduced tiger populations from hundreds of thousands to perhaps fewer than 2,500.
There used to be eight tiger subspecies, but now three of those are extinct due to tigers being hunted as trophies, and also for body parts that are used in traditional Chinese medicine.