The actor, also known for his role in Lost, shared the news on Instagram with a touching photo of him cradling his newborn daughter.
He captioned the shot: "My wife @SandraDurand23 and I are so proud to announce that we became parents yesterday.
"Amélie Moon Durand is here. So grateful and happy:-) #loveandgoodnesstoall."
After being flooded with messages of congratulations, Durand thanked everyone on Twitter.
He wrote: "Thank you kindly for all the well wishes. We are so grateful for all the love."
Durand, 41, married long-term girlfriend Sandra Cho five years ago in October 2010.