Asked by PEOPLE how it felt to be married, Damon flashed his silver wedding band and said, "Great!" before jumping in a car and heading off.
But it was soon back to work for the actor, who headed to the Yonkers, N.Y., set of his CIA thriller The Good Shepherd after his nuptials. "I had to be here today," he told PEOPLE. "I had to come to work."
The newlyweds left for London – where Damon will continue filming – the next day. "I guess we'll have our honeymoon there," Damon told a fan. The couple will have even more reason to celebrate: Bozan is three months pregnant.
Damon pal Marc McGovern told PEOPLE that Luciana is great for Matt. "She's very grounded, very intelligent, very caring" and has adjusted well to his crazy celebrity life. McGovern added that Damon enjoys being a stepfather to Alexia.
This marks the first marriage for the 35-year-old Bourne Identity star and the second for the Argentine-born Bozan, 29, a former bartender who is now an interior designer. (Her married name was Luciana Barroso.) The couple began dating in 2003 when they met in Miami Beach while Damon was filming the comedy Stuck on You.
Bozan, along with Alexia, was at Damon's side throughout the European shoot of his movie Ocean's Twelve. But their big relationship test came over 2004's July 4 weekend, when Damon brought Bozan home to meet his family and friends in Boston.
Like Damon, Bozan also prefers privacy to premieres and paparazzi. "She's not really interested in that stuff," Ocean's Twelve producer Jerry Weintraub told PEOPLE. "She's interested in him."
The interest clearly intensified. In September, the two were engaged. Early that month, at the Venice Film Festival, the actor maintained his usual New England cool even amid buzz that Bozan and he were set to wed. Asked by PEOPLE about the chatter, Damon laughed, held up his ringless finger and declared: "I'm not married yet."
The key word, it turned out, was "yet." In July Damon visited Bellevue, Wash., jeweler Steven Goldfarb and picked a "classic, elegant" platinum ring to have sent to him. "He said he wanted to get the ring and get engaged," Goldfarb told PEOPLE. "He was very pleased."
Damon's brother, Kyle, told PEOPLE at the time: "I am thrilled. I like Lucy a lot. They make a fantastic couple."