NBA's Greg Anthony -- Dishwashes His Way Out of Prostitution Case

9:00 AM PT -- The case against Anthony was officially dismissed Thursday morning.

Greg Anthony's prostitution problems are about to be over ... and it's all because the ex-NBA player (turned NCAA analyst) put in some serious work washing dishes ... TMZ Sports has learned.

As we previously reported, Anthony was arrested for soliciting a hooker at a D.C. hotel back in January ... but struck a plea deal with prosecutors to keep his ass out of jail.

Part of the agreement was that Greg had to serve 32 hours of community service -- which, according to new court docs obtained by TMZ Sports, he completed with a church in Florida.

In fact, the church says Anthony's duties included ...
-- Preparing and serving meals to the homeless
-- Custodial activities in the kitchen and dining room areas (washing dishes)
-- Talking to adults and kids about education and pro sports