In a post on Instagram, the singer is shown holding the babies and also confirmed their names.
Her girl is called "Rumi Carter" and her boy "Sir Carter," ending the speculation.
Earlier this month, the pop diva and her husband, the rapper Jay-Z, whose real name is Shawn Carter, filed for the copyright of the names, ensuring no one else profits from the names to sell anything from fragrances to music.
Their filing with the US Patent and Trademark Office comes from an identical California address to an application for the name of the couple's five-year-old daughter, Blue Ivy Carter.
Rumi is the name of the 13th-century Persian poet who endures as one of the best-loved writers of the Sufi spiritual tradition, with verses that celebrate love, joy and tolerance.
The choice of "Sir" is less obvious, although the two names raise speculation that both children are boys.
Within minutes of posting the photogram on Instagram, it trended on social media, with fans congratulating the singer.
