Corden made the announcement on Twitter on Tuesday, telling followers that he and Carey had "welcomed a beautiful baby girl into the world" earlier that day.
Today we welcomed a beautiful baby daughter into the world. Both she and her mother are doing great. We can't stop smiling. Thank you Harry for stepping in to host the show at 2 and a half hours notice! x x x— James Corden (@JKCorden) December 13, 2017
"Both she and her mother are doing great," the comedian said of his new daughter, adding, "We can't stop smiling."
The baby girl -- whose name hasn't been revealed yet -- joins big siblings Max, 6, and Carey, 3.
The comedian also added in his Twitter message a special note of thanks to musician Harry Styles, who briefly took over "Late Late Show" hosting duties while Corden was with his family. Styles revealed that he was one of the first people to meet the newest little Corden.
"I was just at the hospital before I came to fill in," the singer said, "and she looks a lot like James -- mainly because James looks like a giant baby."
We can't wait to hear more about the little tyke. Congrats to the entire Corden family!
[via: James Corden/Twitter]