updated 01/10/2012 AT 4:00 PM ET
•originally published 01/10/2012 AT 4:15 PM ET
The family left under cover of darkness at 1:30 a.m. Tuesday, the New York Daily News reports.
Observers noted a procession of vehicles with blacked-out windows leaving from the hospital s side gate, reports the newspaper. Two black SUVs helped facilitate the departure, with one blocking traffic so the other could move unobstructed.
“It was the best experience of both of our lives,” Beyoncé and Jay-Z – who has already released a song devoted to his baby girl – said. “We are thankful to everyone for all your prayers, well wishes, love and support.”