The moment was captured on their hidden camera on Sunday night, and took only 6 minutes.
Zookeepers kept the 105 day pregnancy a secret, keeping a careful eye on the first-time mother through hidden cameras.
Zookeeper Paul Kybett revealed that everyone at the zoo was ‘over the moon’ about the latest addition.
‘We were nervous about the pregnancy, as it was Melati’s first cub and we didn’t know how she’d react,’ he admitted.
‘When it came to her due date, we were all watching our monitors with bated breath.
‘The actual birth happened very quickly and Melati’s maternal instincts kicked in immediately as she started licking the cub all over and it soon began wriggling around – we couldn’t have asked for a smoother birth.
‘It’s still very early days, so we’re leaving Melati to take care of her adorable baby, and our cameras allow us to watch them both from a distance. So far she’s proving to be a doting mum.'
Zookeepers do not yet know the sex of the little furball, born just six months after the opening of the zoo's new ‘Tiger Territory’, designed to encourage breeding of the critically endangered sub-species of tiger.
The new mother and baby will have a few weeks of privacy before they are revealed to the outside world.