Entertainment Weekly, Us Weekly and People magazines confirmed the news, but the date of birth and gender of the babies are not yet publicly known.
Beyonce, who is married to rapper Jay-Z, announced her pregnancy in an Instagram photo in February - the most-liked post in history on the network.
The couple already have a daughter, Blue Ivy, aged five.
There has been no official confirmation of the birth from Beyonce and Jay-Z themselves.
