Vonn, who won the gold medal in the women's downhill at the 2010 Olympics before retiring from the sport earlier this year, and New Jersey Devils defenseman Subban confirmed the news in an interview on Vogue magazine's website.
The couple have not set a wedding date, with Vonn saying she just wanted to "enjoy the moment".
"We're not in a big hurry to get married," Vonn, 34, told Vogue.
"It kind of depends on his playing schedule, and when we have time to sit down and go through it. I don't want to stress him out because he has a big season coming."
Subban, 30, proposed at the couple's Los Angeles home, according to Vogue, with an emerald ring.
Canadian international Subban was traded to New Jersey this year after three seasons with the Nashville Predators.