Turns out, Travis Browne was telling the truth ... the UFC star really is in a full blown relationship with Ronda Rousey -- so says Ronda herself.
After Browne went public about it yesterday ... saying Ronda is his woman and he's her man ... Ronda issued a confirmation to ESPN saying, "It's true that Travis and I are in a relationship."
Ronda explained, "I don't talk about my personal life much. That's why it's called 'personal life" ... but added, "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."