It's over for Demi Lovato and UFC stud Luke Rockhold ... the two have called it quits, multiple sources connected to the former couple tell TMZ Sports.

We broke the story ... the two began dating back in the summer after meeting at an MMA gym in L.A. and went public with their relationship in November.

But things didn't work out ... and the two split.

The good news for Demi ... seems she's already rebounding with a new MMA fighter -- Guilherme "Bomba" Vasconcelos ... a Brazilian welterweight who currently fights with Bellator.

In fact, the two spent New Year's Eve together ... and then hit a movie on New Year's Day.

New year, new relationship?