We broke the story ... the former Boston Celtics player was accused of beating the hell out of a man outside Factory nightclub -- causing major injuries.

In fact, the victim was hospitalized for fractures in his face and ribs as well as a broken tooth.

Sources told us ... it all started when Davis almost hit the man with his car -- when the man confronted the NBA player, Davis allegedly picked him up and slammed him on the concrete.

Davis was initially charged with felony assault with intent to cause great bodily injury and faced up to 7 years in prison -- but Wednesday, he cut a deal with prosecutors that will likely keep him out of the big house.

We're told Davis agreed to plea no contest to felony battery -- and in exchange, the assault charge was dropped.

As part of the deal, Davis must complete 320 hours of community labor by the end of 2020 and must pay $104k in restitution to the victim.

If Davis completes those terms, he'll be formally sentenced -- and the judge will decide if he'll get probation. The battery charge will also be reduced to a misdemeanor.