The hairless, pink twins were born to a giant panda Tuesday after being conceived through artificial insemination, and each weigh 150 grams (5 ounces), the zoo said.
It will be a few days before veterinarians can determine their gender.
They are the first pandas born in the Madrid Zoo since it unveiled one named Chu-Lin in 1982 the first panda born in captivity in Europe. That one became wildly popular and a symbol of the Spanish capital.
Spain's National Research Council, which took part in the recent insemination along with scientists from China, said pandas have been born in Europe four times twice in Madrid and two other times in the Vienna zoo.
The council said there are only an estimated 1,600 pandas left living in the wild in China, their numbers depleted by destruction of their habitat.
The Madrid Zoo has four of the endangered animals: the newborns and their parents, mother Hua Zui Ba and father Bing Xing.
That couple was a goodwill gift from the Chinese government to King Juan Carlos and Queen Sofia during a visit to China in 2007.
The zoo used artificial insemination in this case twice, because a first attempt failed because it is extremely difficult for pandas in captivity to conceive naturally.
Being cooped up seems to cause them to "forget how to do it," zoo spokeswoman Amparo Fernandez said.
The new babies' mother, whose name means Flowery Mouth, licked them clean upon birth and the cubs are taking turns being nursed. The one waiting in line is kept in an incubator.
As per panda custom, the father remains aloof and stays away from the babies. This is partly in response to the mother being very protective and keeping her tiny babies from being stepped on or crushed by a dad that can weigh as much as 150 kilograms (330 lbs), Fernandez said.
"The father shows no interest whatsoever," she said. Bing Xing means Star of Ice.