Jameis Winston -- MOPPED LIKE A CHAMP ... During Community Service at YMCA

Jameis Winston mopped, swept and cleaned his ass off at a Florida Y.M.C.A. to complete his community service ... and sources at the center tell TMZ Sports Jameis was a natural.

We've learned ... the Heisman Trophy winner has completed all 20 hours of his required community service stemming from his crab leg theft at a grocery store last week.

Winston decided to put in his time at a Y.M.C.A. in Tallahassee ... where he worked for 5 hours a day for 4 straight days, beginning Thursday night and ending Sunday afternoon.

We spoke with someone at the center who tells us Jameis "put in work" -- cleaning gym equipment, mopping floors, sweeping and other janitorial work.

"He was good, the members loved him ... we were happy to have him."

Now that his comm. service is complete, Winston will NOT face criminal prosecution -- and he's already been reinstated to the Florida State baseball team.