Russell was suspended for 40 games at the end of the 2018 season for violating Major League Baseball's domestic violence policy.
"We decided to non-tender Addison Russell today simply because the role we expected him to play for the 2020 Cubs was inconsistent with how he would have been treated in the salary arbitration process," president of baseball operations Theo Epstein said in a statement, obtained by Jordan Bastian of MLB.com.
"In the year since we decided to tender Addison a contract last November, he has lived up to his promise to put in the important self-improvement work necessary off the field and has shown growth as a person, as a partner, as a parent, and as a citizen. We hope and believe that Addison's work and growth will continue, and we have offered our continued support of him and his family, including Melisa."
In 2017, Russell was accused of domestic violence involving his ex-wife Melisa Reidy - with whom he has a child. After an investigation, MLB suspended Russell for 40 games, which the shortstop did not appeal.
The 25-year-old appeared in 82 games at the major-league level last year after the conclusion of his suspension, and he hit .237/.308/.391 with nine homers and two stolen bases.