"I don't talk about my personal life much. That's why it's called 'personal life,'" Rousey told ESPN in a statement Monday. "It's true that Travis and I are in a relationship. I've really enjoyed the time we have spent together and getting to know one another. And that's all I'm going to say about it."
Earlier Monday, Browne confirmed the relationship in an interview with MMAFightting.com.
"She's my woman, and I'm her man," he said. "There's no boyfriend-girlfriend stuff. There's no dating. We're together."
The two are both training at the Glendale Fighting Club.
"It's not weird," Browne told MMAFighting.com. "It's not something we have to adjust to. We've been doing that the entire time that I was here. She was doing her camps, [and] I was doing mine without that thought process going through our head."
Rumors about the relationship have been flying since August, when Browne's estranged wife tweeted about it while accusing Browne of domestic violence. The UFC hired Las Vegas-based law firm Campbell & Williams to do an independent investigation of the claims and subsequently cleared Browne in late August.
Browne, through his agent, John Fosco, released a statement to ESPN.com after he was cleared in August:
"This two-month period has taught me that strength truly does come from within," Browne said. "Sometimes saying nothing requires more strength than saying everything."
Additionally, Browne said his two sons, Kaleo and Keawe, "have been taught to show women the utmost respect."
In July, Rousey took aim at boxer Floyd Mayweather and his domestic violence history after winning the ESPY award for Best Fighter.
"I wonder how Floyd feels being beat by a woman for once," she said.
The 28-year-old mixed martial artist has become one of the world's most prominent female athletes while winning her past three bouts in a combined 64 seconds. She stopped Bethe Correia in 34 seconds on Aug. 1 and is scheduled to defend her bantamweight title against Holly Holm on Nov. 15 in Melbourne, Australia.
Meanwhile, Browne, ranked by ESPN.com as the No. 8 heavyweight in the world, is scheduled to fight Matt Mitrione on Jan. 17 in Boston.