07/09/2008 at 08:00 PM EDT
Ethan Hawke and girlfriend Ryan Shawhughes were married three weeks ago, a source close to the actor has confirmed to PEOPLE.
Hawke – already the father of two children with his ex-wife Uma Thurman – and the pregnant Shawhughes, described as the former nanny to his children, are also expecting a baby girl, according to the source.
"They were married last month in New York City," according to Hawke's rep, Mara Buxbaum. "No further details are available."
In late January
of this year, Buxbaum said, "I can confirm [the couple are expecting] and they are thrilled."
Speaking in December 2006 about the joys of fatherhood
, the now-37-year-old actor-author said that his two children with Thurman – daughter Maya, now 10, and son Levon, 6 – provide "the greatest pleasure in my life. It's the only role that, if I fail, I will consider my life a failure."
Hawke and Thurman (who recently announced
her engagement to Swiss multimillionaire Arpad "Arki" Busson) split in 2004
, after seven years of marriage.