Us Weekly, Entertainment Weekly and People magazines confirmed the news.
Beyonce announced her pregnancy in an Instagram photo in February – the most-liked post in history on the network.
The singer and her husband, Jay-Z, already have a daughter, Blue Ivy, aged 5.
There has been no official confirmation of the birth from Beyonce and Jay-Z themselves.
Other photos Beyonce posted after her pregnancy announcement showed her swimming under water, reclining on a bed of roses and sitting on a floral throne.
Speculation about the twins’ birth had grown in recent days after a woman was photographed entering a Los Angeles hospital on June 16 holding a card that read “B + J”.
Beyonce is the most-nominated star in the history of the Grammy awards, and her album Lemonade was the world’s best-selling record of 2016.
The singer had been due to headline the Coachella music festival in California in April, but pulled out on her doctor’s advice.
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