Griffey is owed a $4 million buyout, which completes a $116.5 million, nine-year contract that he agreed to with the Cincinnati Reds before the 2000 season.
The 38-year old hit a combined .249 with 18 homers and 71 RBIs in 143 games last season for the Reds and the White Sox. Griffey batted .260 with three homers and 18 RBIs in 41 games with the White Sox, who acquired him July 31 in a trade that sent right-hander Nick Masset and infielder Danny Richar to Cincinnati.
"He was as classy, appreciative and complimentary as a man can be. He said he'd never smiled and laughed so much at the ballpark since he was a kid," White Sox general manager Ken Williams said in an e-mail to The Associated Press. "I wish we could have gone further in the playoffs to enhance those feelings."
Griffey, who agreed to come to Chicago so he would have a chance to play in the postseason, went 2-for-10 in the AL playoffs as the White Sox were beaten in four games by the Tampa Bay Rays. He underwent arthroscopic surgery on his left knee this month to repair torn meniscus and torn cartilage, a condition that affected his power numbers.
"He will undoubtedly help some club, both on the field and in the clubhouse," Williams said. "Pure class."
Griffey passed Sammy Sosa for fifth on the home-run list last season and has 611, trailing only Barry Bonds (762), Hank Aaron (755), Babe Ruth (714) and Willie Mays (660). Griffey is 18th with 1,772 RBIs.
Chicago also declined a $2.25 million option on backup catcher Toby Hall, who batted .260 with two homers in 41 games last season. He gets a $150,000 buyout.
Chicago also agreed to a one-year contract with free-agent infielder Jayson Nix, who spent most of last season with the Colorado Rockies' Triple-A farm club at Colorado Springs. Nix played in 22 games with the Rockies, batting .125 after opening the season as the starter at second base.
Nix gets $400,000 in the majors and $70,000 in the minors.