Williams has a 12-year-old daughter, Matilda, from her 2003-7 relationship with Heath Ledger, who died in 2008, aged 28, from a prescription drug overdose three months after they separated.
Elverum, who performs under the name Mount Eerie, has a three-year-old daughter with wife Geneviève Castrée, who died from pancreatic cancer in July 2016.
In an interview with Vanity Fair, published on Thursday, Williams calls her previously unknown relationship with Elverum “very sacred and very special.”
In July, she said, he left up his home in Anacortes, Washington, and drove across the country to live with her and their daughters in Brooklyn.
“I never gave up on love,” she told the magazine, saying that she has spent the 10 years since Ledger’s death looking for the kind of “radical acceptance” she felt from him.
“I always say to Matilda, ‘Your dad loved me before anybody thought I was talented, or pretty, or had nice clothes.’
“Obviously I’ve never once in my life talked about a relationship. 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. 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.”
Williams said that, in the aftermath of Ledger’s death, she moved to upstate New York to escape the media frenzy. Born in Montana, she said she appreciated the space and freedom.
She moved back to the city six years ago, and has prided herself on keeping a low profile.
“I don’t really want to talk about any of it,” she said. “But there’s that tease, that lure, that’s like, What if this helps somebody?
"What if somebody who has always journeyed in this way, who has struggled as much as I struggled, and looked as much as I looked, finds something that helps them?”
She said that the past decade has taught her valuable lessons about life and love.
“Don’t settle," she said. "Don’t settle for something that feels like a prison, or is hard, or hurts you.