Britney Spears has settled her divorce with Sam Asghari ... this nearly a year after Sam filed to pull the plug ... TMZ has learned.

Britney and Sam filed a Stipulated Judgment, along with her response to Sam's divorce petition, filed by her lawyer, disso queen Laura Wasser. The judge should sign off soon, and when that happens the marriage will official be history.

As we reported, Britney and Sam have a prenup, which essentially leaves Sam with nothing. TMZ broke the story, Britney has paid Sam's rent at his new place. Although we reported earlier the plan was for her to cut him a 6-figure check, we don't know if that happened.

Sam filed back in August -- 14 months after they tied the knot at her Thousand Oaks home -- citing "irreconcilable differences.

There were rumblings from Sam's lawyer, Neal Hersh, that the fitness trainer would contest the prenup, but that didn't materialize.

As for why the marriage fizzled, sources told us Sam believed Britney cheated on him with a staff member at her house ... saying there's footage out there of them in a compromising position.

We were also told Britney had gotten physical with Sam during their time together ... and one time, Brit flipped out and started punching him while he was in his bed. Around the same time as this alleged incident, Sam was spotted with a black eye and bite marks on his arm.

Following the divorce drama, Britney released her memoir, "The Woman in Me" ... and surprisingly, negative talk about Sam was nowhere to be found.

Britney opened up on Instagram in December, saying, "It's so weird being single.  I’ve had a lot of time to really look back with all the good and bad. I’ve realized I don’t talk to myself that nicely at all. I’m easily manipulated and I wear my heart on my sleeve."

BTW, Sam did a shoot with PETA in December, appearing to take a bit of a dig at his failed relationship with Britney -- the pics of him with dogs are captioned, "Some loves last ... never buy dogs, always spay or neuter."

In the meantime ... Sam has been looking fit and cut, living his best life in the gym post-BS.