02/27/2012 at 03:05 PM EST
There's a baby on the way for Uma Thurman.
The actress, 41, is set to welcome her first child with financier Arpad Busson
, a rep for Thurman confirms to PEOPLE exclusively.
Thurman, whose bump went unnoticed when she stepped out for New York Fashion Week
earlier this month, has two children – daughter Maya, 13, and son Levon, 10 – with ex-husband Ethan Hawke
She and Busson, 49, began dating in 2007 and, after a brief split
in 2009, have been together since.
Last June, the couple joined Prince William
at a lavish charity gala at Kensington Palace, an event that marked the Royal couple's official "coming out" as newlyweds. The gala benefited Busson's Absolute Return for Kids (ARK) charity.
Thurman will soon appear in a five-episode arc in NBC's drama Smash