"10-29-2020 Ziggy Blu Ross. Our sweet boy has arrived. I'm over the moon. We are so blessed!" Simpson Ross wrote on Instagram Saturday.
The post included a photo of the sleeping newborn. He is wearing a tiny brown hat and wrapped in a brown blanket.
Ross shared a similar message and the same photo on his own account.
"I'm in Heaven," Ross said.
The couple, who married in 2014, announced in May they were expecting their second child.
They are also the parents of a 5-year-old daughter named Jagger Snow.
Simpson Ross, 36, also has a 12-year-old son named Bronx Mowgli with her ex-husband, rocker Pete Wentz.
Ross, 32, is the son of music icon Diana Ross and the brother of actress Tracee Ellis Ross.