The couple sparked rumours of a romance after Corden escorted the singer home from a Teenage Cancer Trust comedy gig last week.
He told the Sunday People: "Yes, we're together and I'm smitten. She is a great girl - we get on really well and have such a laugh together."
The pair hit it off when Corden appeared on Allen's chatshow last month. He later revealed that he wants her to guest star on his BBC Three comedy Gavin & Stacey.
Allen split with Chemical Brothers star Ed Simons in February, just weeks after suffering a miscarriage.
> Lily Allen annoyed over comedy gig reports