The twins were born at a Long Island hospital on February 22.
They arrived a day after both their parents were named winners of Latin music's "Premio Lo Nuestro" awards. Lopez won for best solo pop singer, while Anthony was named salsa artist of the year.
Lopez's manager, Simon Fields, tells People that Lopez is "thrilled" about the babies' arrival. At 39, she's a mother for the first time.
Anthony, who is 38, has three other children.
The couple wed in 2004.