According to new legal docs, obtained by TMZ, the judge signed off the settlement reached by Steve and his now-ex-wife, Sheree Gustin, on Wednesday ... agreeing to joint legal and physical custody of their two minor children, Jack and Brooklyn.

Steve's paying Sheree $12,500 per month for child support ... $10,000 for 9-year-old Brooklyn and $2,500 for 17-year-old Jack.

When Jack turns 18 at the end of March, Steve's child support obligations to him will go away ... but he’ll continue to fork over the $10K for Brooklyn until she turns 18.

Steve and Sheree also agreed to waive any and all rights to spousal support ... but he's going to pay her $50,000 in $ 2,500-per-month installments.

TMZ broke the story ... Steve filed for divorce in July 2022 after 23 years of marriage, only two months after he claimed Sheree was having a baby and he wasn't the father.