The tiny cub -- pink, hairless and only about the size of an adult mouse -- was born at 5:35 pm (2134 GMT), the zoo said in a statement, and Mei Xiang reacted by picking up the cub.
"All of us are thrilled that Mei Xiang has given birth. The cub is vulnerable at this tiny size but we know Mei is an excellent mother," zoo director Dennis Kelly said.
The new mother was artificially inseminated in April with frozen semen from a male giant panda named Hui Hui that resides at the China Conservation and Research Center for the Giant Panda in Sichuan province.
She was also inseminated with fresh semen from the zoo's male giant panda Tian Tian. DNA tests will establish which is the father.
But she also lost at least two other cubs, one that was stillborn in 2013 and another that lived just six days in 2012.
This year, Mei Xiang exhibited signs of pregnancy in July that included sleeping more, eating less, building a nest and spending more time in her den.
The zoo said Mei Xiang will spend almost all her time in her den for the next two weeks. The enclosure will be closed to provide quiet, though online "panda cams" provide a video stream of the creatures.
On Tuesday, Malaysia announced that a giant panda at its National Zoo, Liang Liang, had given birth. The newborn's sex has yet to be determined.
There are fewer than 2,000 pandas now left in the wild, according to the World Wildlife Fund, as their habitats have been ravaged by development.
Roads and railways cut through the bamboo forests they depend upon in China's Yangtze Basin, their primary habitat.
Pandas rely on bamboo and eat almost nothing else. Given their low birthrate, captive breeding programs are key to ensuring their survival.
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