After months of speculation, UFC heavyweight Travis Brownehas confirmed it. He is indeed in a romantic relationship with UFC women's bantamweight champion and general A-list celebrity Ronda Rousey.  
Browne confirmed it this in an interview (warning: NSFW language) with Ariel Helwani of MMAFighting.com during Monday's installment of The MMA Hour.
Update, 11:52 PM EDT
Rousey has co-signed his statement, and said that she is indeed in a relationship with Browne.
"I don't talk about my personal life much, that's why it's called 'personal life,'" Rousey told Ramona Shelburne of ESPN. "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."
--End of Update--
While Browne refused to say they were dating, he flatly stated, per Marc Raimondi of MMAFighting.com, "She's my woman, and I'm her man. There's no boyfriend, girlfriend stuff. There's no dating. We're together."
The two have been rumored to be a couple since August, when Browne's estranged wife, fitness model Jenna Renee Webb, accused the two of seeing one another. Worth noting, this all occurred while Browne was being investigated by the UFC for domestic violence due to accusations made by his wife on Instagram. While Browne came out of the UFC's investigation unscathed, Webb has stood by her claims.

Ronda Rousey Has a New Boyfriend in the Form of UFC Heavyweight Travis Browne

After months of speculation, UFC heavyweight Travis Brownehas confirmed it. He is indeed in a romantic relationship with UFC women's bantamweight champion and general A-list celebrity Ronda Rousey.  
Browne confirmed it this in an interview (warning: NSFW language) with Ariel Helwani of MMAFighting.com during Monday's installment of The MMA Hour.
Update, 11:52 PM EDT
Rousey has co-signed his statement, and said that she is indeed in a relationship with Browne.
"I don't talk about my personal life much, that's why it's called 'personal life,'" Rousey told Ramona Shelburne of ESPN. "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."
--End of Update--
While Browne refused to say they were dating, he flatly stated, per Marc Raimondi of MMAFighting.com, "She's my woman, and I'm her man. There's no boyfriend, girlfriend stuff. There's no dating. We're together."
The two have been rumored to be a couple since August, when Browne's estranged wife, fitness model Jenna Renee Webb, accused the two of seeing one another. Worth noting, this all occurred while Browne was being investigated by the UFC for domestic violence due to accusations made by his wife on Instagram. While Browne came out of the UFC's investigation unscathed, Webb has stood by her claims.