The couple, who tied the knot last September, welcomed their first child on June 19, reported People magazine.
"They both couldn't be happier," a source said.
After announcing the pregnancy in January, Sims, 39, informed about the sex of the baby in April.
"I am a little nervous about the delivery and breastfeeding. I hope I can do it, I hope we come through. I am so excited to meet him and just hold his hand," she had said.
