03/11/2009 AT 02:15 PM EDT
and Ryan Adams are now husband and wife.
The couple, who got engaged
just last month, tied the knot in Savannah, Ga., Moore's rep confirms to PEOPLE.
The singer-actress, 24, and Adams, 34, applied for a marriage license on Tuesday afternoon at the Chatham County Probate office in Savannah, according to a court source, who adds that the famous couple went unrecognized.
Moore tells Marie Claire
in its April issue that her now rocker husband is "a good egg. I'm in awe of him: his brain, his passion. He's truly one of a kind."
was the first to report news of the marriage.
Reporting by ALEXIS CHIU and POLLY STRAMMRELATED GALLERY:
Photos: Surprise! We're Married!RELATED ARTICLES:
2007: Mandy spills on surviving teen stardom
2002: Mandy makes PEOPLE's Most Beautiful list!