Jay-Z was present at the birth, and the couple are claimed to have hired the entire fourth floor of the hospital at a cost of £840k.
Bey had checked in under the name Ingrid Jackson and security is reported to have been tightened for her stay at the facility.
The news has been reported by a number of media sources, including the Rihanna tweeted: "Welcome to the world princess Carter! Love Aunty Rih."
And DefJam music mogul Russell Simmons posted: "Congrats to my good friends Beyonce and Jay-Z."