Husband Pete Wentz was present as Simpson went into labour in a Los Angeles hospital.
The couple have named their son Bronx Mowgli Wentz, who was born weighing 7lbs, 11oz.
"Ashlee, Pete and baby Bronx are all healthy and happy, and thank everyone for their well wishes!" a representative for the couple told People.
Earlier in the week, sister Jessica Simpson claimed the couple wanted to induce labour as Simpson was so eager to give birth.