Barroso, who Damon proposed to shortly before America's Labor Day holiday (05SEP05), is three months pregnant, according to US TV show Access Hollywood.
The child will be Damon's first - Barroso has a six-year-old daughter, ALEXA, from a previous relationship.
The news comes just one week after Damon talked about his desire to be a strong father figure.
He said, "I have longed for (kids) in real life, anyway. I just have to learn how to be a disciplinarian.
"Now I'm good at winding kids up, but I'm not so good at chilling them out."