Eleven-year-old mum Shin Shin gave birth just before noon, officials at Tokyo's Ueno Zoo said in a statement.
Pandas are born pink, hairless and weighing around 100 grams (three-and-a-half ounces) - so small it can be difficult to determine their sex.
"There have been cases where the sex of a panda has been found to be wrongly determined several years after its birth," a zoo spokesman told AFP amid the panda-monium.
"It could take a while before we know."
Shin Shin, who mated with male Ri Ri in February, had another baby in 2012 - the first time at the zoo in 24 years, but the cub died from pneumonia six days later.
Footage from a camera inside the panda enclosure showed the moment of birth, when the screeching noises of the tiny baby could clearly be heard as Shin Shin scooped it up with her mouth.
Zoo officials were not immediately able to give exact details about the size and weight of the cub as the proud mum, who tips the scales at 110 kilograms (240 pounds), protectively cuddled her new-born baby.
"Most of the time the mother has been cradling her baby so we haven't been able to measure it precisely," a spokeswoman told AFP.
"It's almost impossible to see the baby when she's being hugged by mum but we estimate it at about 150 grams."
As a mother-to-be, Shin Shin delighted huge crowds of well-wishers in Tokyo last month as she sat lazily munching on bamboo and playfully rubbed the husks on her furry belly before being moved into confinement.
Considered an endangered species, it is estimated fewer than 2,000 giant pandas remain in the wild, in three provinces in south-central China.
Giant pandas are painfully bashful animals and clumsy lovers, with males often miscalculating when a female is in the mood for love and frequently baffled by the mechanics of mating, according to experts.
In the event the cuddly creatures do feel a romantic spark, sex is frequently over too quickly to impregnate the female, who is only receptive to the proposition for two or three days a year between February and May.
Shin Shin's happy news was broadcast on national television and has already had an economic impact on local businesses, with one Chinese restaurant's shares soaring by 38 percent in response.
The Totenko chain, whose main outlet is near the zoo, already reported a jump last month on news of a possible pregnancy.
The birth could also potentially help thaw the often frosty diplomatic relations between Japan and China as Beijing caught the celebratory mood.
"Giant pandas are always messengers of friendship from China towards other countries," said foreign affairs ministry spokesman Lu Kang.
"We also hope giant pandas can play a greater role to promote the affection between Chinese and Japanese people."
Tokyo governor Yuriko Koike also expressed her delight, telling local media: "Romance is not just restricted to humans."
Meanwhile, Japanese Chief Cabinet Secretary Yoshihide Suga, the government's top spokesman, showed his softer side as he weighed in on the day's top feel-good story.
"It is news that will brighten the whole country," he told a daily news briefing. "I wonder why pandas are so popular. It's probably their cute faces and adorable gestures."
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