Huma Abedin and Anthony Weiner Settling Divorce Out of Court

Huma Abedin and convicted sex offender Anthony Weiner signed docs to call off their divorce -- but they're still done ... they're just taking a quieter approach.

Hillary Clinton's trusted aide, Huma, had a divorce hearing scheduled Wednesday morning, but instead submitted docs to nix the divorce case. Both Huma and Weiner signed the docs.

Huma's attorney, Charles Miller, tells TMZ ... “In order to reduce any impact of these proceedings on their child, the parties have decided to reach a settlement swiftly and privately.”

In other words ... they're going to avoid feuding -- in court or in public -- and hammer out a divorce settlement privately. They'll still need a judge to sign off eventually.

As we reported ... Huma filed for divorce back in May 2017 following Weiner's guilty plea for sexting a 15-year-old girl. He's currently serving a 21-month prison sentence.