Sunderland had been seeking up to £1.5 million ($2.18m, B2.14) in compensation from Nunez, his agent Pablo Bentancur and his former club.
Sunderland claimed they only discovered to their cost after paying out for Nunez, that his former club was the third division Uruguay Montevideo, not the more celebrated side, Nacional Montevideo.
The English club claimed it was given false information about the playing credentials of Nunez, who played just 44 minutes of first-team football after it paid £1.1m ($1.59m, B1.76) for him in March 2000.
Sunderland made a further payment of £350,000 ($506,770, B559.080) for the 28-year-old Honduras international, whose former clubs also include PAOK in Greece.
Sunderland had launched the court action against Uruguay Montevideo FC, Nunez and Bentancur, but at a 20-minute hearing on Monday, the judge was told the parties had reached a settlement.
Outside the court, the club's lawyers said they were unable to reveal the terms of the settlement.
