Damon, 35, and his bride exchanged wedding vows during a small ceremony at an undisclosed location, spokeswoman Jennifer Allen said. Bozan's 7-year-old daughter witnessed the ceremony. In a previous marriage, Bozan went by the name Luciana Barroso.
The wedding took place in New York's City Hall, according to Ed Skyler, a spokesman for Mayor Michael Bloomberg.
Skyler and Damon's publicist provided no further details.
Asked if Damon's friend, actor Ben Affleck witnessed the wedding, Allen said no.
It was the first marriage for Damon, the second for Bozan. They will split their time between homes in New York and Florida.
Damon's publicist wouldn't discuss an "Access Hollywood" report that the new Mrs. Damon is pregnant.
The Oscar-winning "Good Will Hunting" screenwriter and actor ("Saving Private Ryan," "The Talented Mr. Ripley," "Ocean's Twelve," "Syriana") met Bozan while she was working as a bartender in Florida, Allen said.
Damon is in New York shooting the Robert De Niro-directed film "The Good Shepherd" with Angelina Jolie.