Court records we've obtained show Payne cut a deal with prosecutors on Monday to put everything in his rearview mirror ... agreeing to plead guilty to one misdemeanor count of false report to law enforcement.

In exchange, officials dismissed the refusal to provide truthful name charge he had also been facing.

Specific details surrounding his sentencing were not made immediately available ... although a court official tells us fines were involved.

Payne, of course, was first charged in the case back in June ... after cops said the 30-year-old basketball player would not tell them the truth when they asked for his identity at his Scottsdale, Ariz. home.

Officers say during questioning about a potential domestic disturbance, Payne repeatedly told them he was "Terry Johnson" ... and when he finally admitted he was actually "Cameron Payne," body camera footage shows they arrested him and called his decision to lie "dumb."

Despite the legal case, Payne has played in 20 games for New York this season ... including Sunday's matchup with the Magic, where he logged two rebounds and two assists in 10 minutes.