Corden apparently proposed to Carey, who is pregnant with the couple's first child, on Christmas Day.
"James was down on one knee, it was Christmas Day and there were tears shed," a source told The Sun. "It was magical."
The Gavin & Stacey star has set the wedding date for 2012 and has told friends to set aside four weeks for the stag party.
Corden has been dating former TV producer Carey - who now campaigns for Save The Children - for almost a year.