The actor and his wife Celeste welcomed daughter Brylee Bea on 19 February (15), but Baumgartner did not share the happy news until Tuesday (24Mar15) - the 10th anniversary of the premiere of the U.S. version of The Office.
After sharing old photos from his time on the Emmy Award-winning sitcom on Instagram.com, he posted the first photo of his baby girl as she napped in his arms.
He added the caption, "My latest project. 9 months in the making. I am happy to announce the arrival of my daughter- Brylee Bea- healthy and very happy. She told me she looks forward to catching up on all the old episodes of The Office once her eyes adjust to life."
This is the first child for the Baumgartners, who wed last April (14) in their Los Angeles home.