The first twin weighed 180 grams and the second 140 grams, the zoo said.
"Both the mother and the twin pandas are in good health," a representative from the zoo said in a statement.
"Ai Bao is taking good care of her cubs, putting her experience with Fu Bao to use."
Fu Bao, born in July 2020, is the twins' older sister and the first giant panda born in South Korea through natural breeding.
The YouTube video of the twins' birth has garnered 640,000 views since it was uploaded, with viewers gushing about the arrival of the cubs.
"Welcome to the world, sweet babies! Congrats to the Bao family and thanks to the grandpas and all the staff taking care of them," wrote one viewer.
Another commented: "Tears keep on running from my eyes because I'm so proud of Ai Bao! Well done, Ai Bao!"
Ai Bao and Le Bao, the father, arrived in South Korea in 2016 as a state gift from Chinese President Xi Jinping.
China has long deployed "panda diplomacy", gifting the animals to various countries, often to further its foreign policy aims.
Beijing only loans pandas to foreign zoos, which must usually return any offspring within a few years of their birth to join the country's breeding programme.
