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The couple have been dating since 2003, when they met in Miami Beach while Damon was filming the comedy Stuck on You.
It will be the first marriage for the 34-year-old Brothers Grimm star. Barroso, 29, a former bartender who is now an interior designer, has a 7-year-old daughter, Alexia, from a previous relationship.
The Argentine-born Barroso, along with her daughter, was at Damon's side throughout the European shoot of Ocean's Twelve, PEOPLE reported last year. But their big relationship test came over 2004's July 4 weekend, when Damon brought Barroso home to meet his family and friends in Boston.
Introducing her to pals at a local restaurant, he kissed her "every five seconds," said friend Jamal Prince. "He's very serious about her. In the past he kept the other ones secretive. This one he's not hiding."
Like Damon, Barroso also prefers privacy to premieres and paparazzi. "She's not really interested in that stuff," Ocean's Twelve producer Jerry Weintraub told PEOPLE last year. "She's interested in him."
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