The 31-year-old "Tangled" star split from her husband rocker Ryan Adams in January, just weeks before their sixth wedding anniversary, citing "irreconcilable differences" for the breakup, but the pair was keen to stress the separation was amicable.
Moore is now dating folk-rock star Goldsmith, and she apparently confirmed the speculation by posting a photograph on Instagram, showing him playing Scrabble, reported Us magazine.
Moore added the caption, "Flashback to last week when my 52 point word befuddled both of us," alongside an image of a pink heart.
She has also been spotted at several Dawes gigs, and shared shots of the band performing earlier this month.