Jones, who is scheduled to become a free agent, was told of Atlanta's decision to move on without him after a meeting with Braves General Manager John Schuerholz Tuesday morning, according to the Braves' Web site.
Jones, a nine-time Gold Glove winner, had his worst season in Atlanta this season, hitting just .222 with 26 home runs and 94 runs batted in 154 games.
Atlanta's Web site also reported Jones' agent, Scott Boras, is looking for at least a five-year deal for his client and an annual salary of about $20 million.
Jones, 30, has been with the Braves since 1996 and was a standout in center field the last 12 seasons. In 1,748 career games, Jones is a .263 hitter with 368 homers and 1,117 RBI. He also scored 1,045 runs and had 330 doubles. Jones also committed just 44 errors in those 12 seasons, including just six over the last three seasons.