Fetty and Leandra Gonzalez agreed to a divorce settlement and the judge signed off on it on September 4 to make it official ... this according to legal docs obtained by TMZ.

The rapper and Leandra got married August 3, 2019 ... so their marriage survived a little over a year. They had no kids and the terms of their settlement are under wraps.

Leandra, who filed for divorce in March, alleged in legal docs Fetty was a booze-hound and abusive cheater. She claimed Fetty was physically abusive less than a month after getting married in Toronto. She also alleges Fetty cheated on her multiple times with several women ... including going on a trip to the Bahamas on New Year's Eve with another woman. Fetty denied all of the allegations.

Either way ... they can finally put their divorce drama behind them.