Ceren Alkac and Jason Lee

Some celebrities are better at keeping secrets than others. Jason Lee must be one of the good ones.

The My Name is Earl star let the news slip to Sydney's Sun Herald that he and Ceren Alkac, the mother of his second child, are married. "My wife is Australian. And she is my wife now 'cause we just got married, and you can report that!" he says.

Lee's rep confirmed the news to Us, adding that the couple married in California in July, a month before Alkac gave birth to a baby girl. The not-so newlyweds have yet to reveal their daughter's name publicly.

Lee was married to photographer Carmen Llywelyn from 1995 to 2001 and engaged to Beth Riesgra, the mother of his 5-year-old son, Pilot Inspektor.