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.
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 naked on a floral throne.
In one, the 'Lemonade' singer stood naked, cradling her belly with one hand and a breast with the other, next to the sculpted head of an Egyptian ruler.