FINALLY ... Luke Rockhold and Demi Lovato have gone public with their relationship -- hitting up an NFL game as a couple this weekend ... and we got the pic.
TMZ Sports broke the story ... Luke and Demi began quietly dating at the beginning of the summer after hitting it off at the Unbreakable MMA gym in L.A.
There was some secret social media flirting ... but for the most part, they kept things on the D.L. -- until Sunday when they arrived to the L.A. Rams game together and even posed for pics.
We're told things are going really well so far ... (for the couple, not the Rams).