James and his wife Julia welcomed their daughter into the world last week and have since been inundated with well-wishes.
The Gavin and Stacey star has now taken to Twitter and told his followers that the arrival of their baby girl has made his family "complete".
In a heartfelt tweet, James said: "Thanks for all your kind messages about the birth of our daughter. She's beautiful and has made our family feel happy and complete x."
James and Julia are already parents to a three-year-old son called Max. The couple are yet to confirm the name of their newest addition.
Thanks for all your kind messages about the birth of our daughter.She's beautiful and has made our family feel happy and complete x— Jkcorden (@JKCorden) November 1, 2014
It's a busy time for James at the moment. Along with a family life - which will now include late-night feeds and nappy changes - he has recently landed a new job Stateside.
Next year, James will replace Craig Ferguson as host on The Late Late Show in America.
After news of his new role was announced, James said: "I can't describe how thrilled and honoured I am to be taking over from the brilliant Craig Ferguson.
"I can't wait to get started and will do my very best to make a show America will enjoy."
Celebrities who have welcomed babies in 2014:
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