Son Liam James Ferguson was born Monday, Jan. 31 in Los Angeles, a rep for The Late Late Show host confirms to PEOPLE exclusively.
"Everyone is happy and healthy," says the rep. "The family is doing great, everybody's perfect."
Ferguson, 48, and his wife, an art dealer, tied the knot in December 2008. Ferguson is already dad to Milo Hamish, 9, his son from a previous marriage.
Reporting by JD HEYMAN