The couple, who met in 2003 and got married in 2005, already have another daughter called Isabella, who is aged two, and Mrs Damon has 10-year-old Alexa from a previous marriage.
Their relationship had started when she was working as a bartender in Florida and 37-year-old Matt Damon was in the location being filmed for Stuck On You.
Damon rose to international fame after he was in the 1997 film Good Will Hunting, which he had co-written and starred in with actor friend Ben Affleck.
After that he went on to gain much critical acclaim for other films such as The Talented Mr Ripley and Saving Private Ryan.
