"Words cannot explain how happy we are to welcome our beautiful son into our family," Kerr and Spiegel said in a statement to People.
"Miranda is doing well and Flynn is excited to be a big brother," the couple added. "Thank you for the kind words and wishes during this very special time."
Sources said Kerr and Spiegel named their son Hart after Spiegel's grandfather. The couple had announced Kerr's pregnancy in November after marrying in May 2017.
"Evan and I have been together for a while, and [Flynn] was like, 'When am I going to have a little baby brother or sister?' I'm like, 'Look, we've got to get married first,'" the model recounted on Jimmy Kimmel Live in February.
"So the day after the wedding he comes running in and he's like, 'Mommy, is it in there?' I was like, 'Honey, give it a minute,'" she said.