Jones, 34, will have a chance to make the Nets in training camp. Brooklyn has 12 guaranteed contracts, and several players on partial guarantees, including Markel Brown, Quincy Miller and Ryan Boatright.
Jones is familiar with Nets coach Lionel Hollins, who was a Memphis assistant during Jones' stint with the team from 2003-07.
After starting the season in the NBA Development League a year ago, Jones signed with the Los Angeles Clippers and appeared in 33 regular season and 11 playoff games. Across 11 NBA seasons with seven teams, Jones has averaged 5.4 points.