Corden was nominated in the category 'Best Performance By An Actor In A Leading Role In A Play' for his performance in the Broadway production of One Man, Two Guvnors.
The actor, who starred in the show on the West End last year, won in his category against Philip Seymour Hoffman, James Earl Jones, Frank Langella and John Lithgow.
An emotional Corden first acknowledged his fellow nominees, saying: "John Lithgow and James Earl Jones and Frank Langella - and my favourite actor in the world, Philip Seymour Hoffman - to be on a list with you was enough, and holding this honestly just reminds me there is no such thing as 'best'. Honestly, I am overwhelmed."
The Gavin & Stacey star also thanked his girlfriend Julia Carey, with whom he recently welcomed a baby son.
"My girlfriend Julia gave birth to our son like, five days before we started rehearsals," Corden said, "She's my baby mama, and I can't wait to marry her. Seriously, I would not be holding this if it wasn't for her.
"She makes me say 'us' instead of 'I' and 'we' instead of 'me', and I love her. Thank you very much."
Watch James Corden's Tony Awards acceptance speech below: