The news comes after Williams was spotted without her wedding band at several public outings.
"Michelle and Phil separated at the beginning of the year. It was an amicable spilt and they remain friends," a source close to the situation told People.
Williams, 38, revealed her marriage to Elverum, 40, in a July 2018 interview with Vanity Fair, sharing that they had quietly tied the knot in the Adirondacks earlier that month.
"Obviously I've never once in my life talked about a relationship," she said, telling the outlet that the indie musician moved from Washington to Brooklyn, New York, to live with her. "But Phil isn't anyone else. And that's worth something."
"Ultimately the way he loves me is the way I want to live my life on the whole," she added. "I work to be free inside of the moment. I parent to let Matilda feel free to be herself, and I am finally loved by someone who makes me feel free."
The pair was photographed for the first time together in upstate New York last September.
Williams was previously in a relationship with Heath Ledger, who died in 2008 following an accidental drug overdose. The pair shared a now 13-year-old daughter, Matilda. Elverum's marriage to Williams was his second. He was previously married to Genevieve Castree, who died in 2016. The two shared a now 3-year-old daughter, Agathe.