The Cordons are already parents to six-year-old Max and two-year-old Carey.
Corden, who hosts ‘The Late Late Show’ in the US, has previously spoken out about how becoming a father changed his perspective on life.
“It’s great – you really can’t understand in advance quite how happy [children] make you and you don’t realise you could have such a depth of feeling for people,” he told the Daily Record in 2013.
“You spot so quickly the indifference of friends of yours who don’t have children.”
Congrats to the couple!