Annette filed divorce docs Tuesday in Suffolk County, NY and, according to court records, Matt's not contesting. Makes sense ... last month, the couple reportedly hammered out a settlement that has her walking away with $20 million in assets. 

It's unclear exactly how they're splitting up their properties -- they've got a ton in NY state and even New Zealand -- but the NY Post reported Annette's getting their horse farm in the Hamptons.

The couple split up back in 2017 after Matt was fired from 'Today' over a slew of sexual harassment allegations at NBC. 

Matt and Annette, and of course their lawyers, hashed out the division of their assets in private before filing the paperwork with the court. Annette's attorney, John Teitler, confirms to TMZ that the matter has been settled.

Now, they just need the judge to sign off and they'll be ready to mingle, as they say. Court officials say there's no timeline on when they'll get that stamp of approval -- there's no waiting period, it just depends on the judge's workload.