Lee is best known for his roles on the TV sit-com "My Name is Earl" and in the films "Chasing Amy," "Dogma," "Almost Famous," "Vanilla Sky," "Underdog" and "Alvin and the Chipmunks."
"I am able to confirm that Jason Lee and Ceren Alkac were married in July 2008 in California," the actor's representative told People magazine.
Lee and Alkac are the parents of a daughter born in August. The infant's name has not been released to the public.
The actor also has a 5-year-old son, famously named Pilot Inspektor, from his previous relationship with actress Beth Riesgraf.