The League Two club had been holding on to his registration after the defender walked out on Meadow Lane just one game into his four-year deal.
The move opens the way for the 35-year-old to sign for Newcastle United, where the manager, Chris Hughton, last month said that the former England defender still "has a lot to offer the game".
The Professional Footballers' Association chief executive, Gordon Taylor, told BBC Sport: "Sol Campbell is now a free agent. His contract dispute has been resolved and he is free to pursue football in the January transfer window. He can sign for any club he wants now."
Although free to sign with a club, Campbell is not expected to play until January.