The exes got the judge's stamp of approval Tuesday. We broke the story ... Brian and Megan hashed out the agreement back in October, and were just waiting for the court to make it the real deal.

Remember, the divorce settlement said they agreed to joint legal and physical custody of their 3 boys ... and while the docs didn't say much about child and spousal support, there was a reference to a settlement agreed upon outside of court.

Sources connected to the former couple told us they did not have a prenup ... and in California, that means anything they acquired during their 10-year union would be 50/50.

Megan's also having her legal name reverted back to Megan Fox from Megan Green.

Megan and Brian got hitched on a Maui beach in 2010, and she filed for divorce in 2015, but the papers were eventually withdrawn in 2019.

She filed for divorce again in November 2020, and this time they took it all the way through to the end.

As you know, both Megan and Brian have already moved on.

Megan got engaged to Machine Gun Kelly just last month, and they allegedly celebrated by drinking each other's blood.

Brian had a few flings, but now he's dating Sharna Burgess ... and they're expecting their first child together.