The new arrival was born on Sunday 30 March to parents Kamili and Gugas, however during the early weeks newborn gorillas cling to the mother's stomach, making it difficult for zoo keepers to find out the infant's gender.
Kamili was so protective that it was impossible to determine whether or not the baby was a boy or a girl.
After weeks of waiting, the zoo has now announced that the infant is a girl and, after much consideration, she has been named Kibibi which means 'little lady' in Swahili.
Zoo curator, Julie Mansell, said: "Kibibi is the second arrival within the last year for dad, Gugas, and she is the first girl!
"In 2012, with no sign of pregnancies, we tested Gugas' fertility and the results were not promising. In fact, we feared that Gugas would never father any young. We are delighted that he has proven us all wrong with the arrival of Kibibi and Baako in the last year."
Gugas was born in the wild but had an unfortunate start to life as his parents were killed, probably for bush meat.
As a young, orphaned gorilla, he was acquired by a Portuguese circus and became very ill.
He was abandoned at the gates of Lisbon Zoo and was then moved to Stuttgart Zoo to live in a nursery group for orphaned gorillas.
He arrived at Belfast Zoo in 1998 and is genetically very important to the European breeding programme as, until this year, he was not represented in the zoo population.
Julie continued: "All apes are endangered or critically endangered and some professionals have even predicted that all species of ape will be extinct within 30 years.
"Gorilla populations have declined by more than 50% in recent decades and our role, as a zoo, in their conservation is becoming more and more vital."