The child, who was born Thursday night, is the first for Simpson-Wentz and her husband Pete Wentz, the bassist for the pop-punk group Fall Out Boy.
"Ashlee, Pete and baby Bronx are all healthy and happy, and thank everyone for their well wishes!" a representative for the couple told the magazine.
Simpson-Wentz is the younger sister of singer-actress Jessica Simpson.
Pistorius testifies he didn't consciously pull trigger when he shot girlfriend
'Happy' fan videos make Pharrell cry [VIDEO]