Wilkes' wife Nikki gave birth to Mickey, the couple's first child, weighing 7lb 15 oz, on Tuesday morning.
"Nikki and Mickey are doing great," said Wilkes. "He was born this morning at 7.20am and I fainted at 7.21am. We are both so happy and can't wait to get our new family back home."
The former You've Been Framed host, 27, grew up with Williams in Stoke-on-Trent. He previously revealed: "Rob was the first to know about the baby and of course he's going to be godfather. He's my best mate."