Jeezy & Jeannie Mai's Divorce Finalized After Nasty Back and Forth

Jeezy and Jeannie Mai's divorce is in the books -- 'cause they've come to a settlement ... and they're going out of their way to keep the details under wraps.

According to new court docs, obtained by TMZ, the two exes -- who've been squabbling A LOT lately over child custody, claims of abuse and other ugly tidbits -- have settled their divorce ... and not just that, they've filed to wrap up the whole thing under seal so the details won't be public.

Of course, there was a ton of back and forth over the past few months -- with Jeezy alleging Jeannie was keeping their daughter from him and making his parenting time with their kid incredibly difficult ... and JM fired back, suggesting Jeezy kept guns around in a way that wasn't safe with a child around ... and also made big DV claims against him.

You'll recall ... she alleged abuse against Jeezy, claiming he'd gotten physical with her in the past. Jeezy denied all her claims ... and vowed to fight for the truth in court.

While it seemed like this thing was going to drag out for a while in the public eye -- Jeezy and Jeannie have now settled the case and got an order allowing them to place all the docs under seal.

Therefore ... the details of their settlement will remain hidden from public view, including any terms about custody/child support, property splits and/or spousal support.

It's been a long saga ... but it's all over now, and they're officially unattached in the eyes of the law.