The 40-year-old actor and his wife Ryan Shawhughes - who got married in June 2008 - welcomed their second child, a baby daughter named Indiana, into the world two weeks ago, and the couple are said to be "very happy" at their new arrival.
An onlooker at New York's Maritime Hotel explained the star - who also has a three-year-old daughter, Clementine Jane, with Ryan - looked "proud" as he dined with his family on Friday
The source told People.com: "He was very happy. Seemed like a proud daddy."
Indiana's arrival marks the fourth time Ethan has become a dad, with the star also fathering 13-year-old Maya and nine-year-old Levon, his two children with ex-wife, actress Uma Thurman.
Ethan has previously admitted being a father is his "greatest pleasure in life".
He said: "It is the greatest pleasure in my life. It's the only role that if I fail, I will consider my life a failure."
Labels: Ethan Hawke, Hollywood