Josh Brown's marriage to the woman he admittedly abused is finally over -- and he's going to be paying her A LOT of money ... this according to court docs obtained by TMZ Sports.
The docs show Molly Brown separated from the ex-New York Giants kicker on May 22, 2015 ... the same day he was arrested for domestic violence.
That charge was eventually dropped. Brown admitted to "abusing" his wife but later insisted the abuse was NOT physical.