A clerk for Granite County confirms to PEOPLE that the couple married Oct. 1 in Philipsburg, Montana.
Rumors that the stars had secretly tied the knot began when a report surfaced over the weekend that the new parents quietly exchanged vows after welcoming their first child, daughter Rose Dorothy, in September. News of their nuptials comes just after the actress was spotted earlier this month wearing what was speculated to be a wedding band at a fundraiser for Hurricane Sandy victims.
A rep for Johansson declined to comment.
"They kept the wedding a big secret because they both wanted privacy," a source told the New York Post, adding that the ceremony was held in the States.
News of their plans to wed broke in September 2013 with a source telling PEOPLE, "They're engaged and very happy."
Just six months after the proposal, the actress, 30, had even more happy news to share: her pregnancy.
A secret ceremony should come as no surprise: When asked whether she planned on settling in the United States or her beau's native France, Johansson told Craig Ferguson in March, "I've been thinking lately that maybe it's good to move to some faraway country where you can ski."
She added to WSJ Magazine of her life plans: "There must exist a world in which I can balance those things, be able to raise a family and still make a film a year, or work on my own, develop things, do theater. I want to be able to have it all."
Reporting by MARIAH HAAS and MICHAEL MILLER