The team announced that he will receive $500,000 this season. The White Sox have a $3.5 million option for 2013 with a $500,000 buyout.
"We were aggressive," White Sox assistant general manager Rick Hahn said. "For reasons that I think he fairly clearly outlined at the time, he decided to go with the opportunity on the North Side over ours."
With the Cubs, Fukudome could remain in right field. The White Sox had Jermaine Dye in place at the time.
The Cubs signed the former Japanese League MVP before the 2008 season to a four-year, $48 million deal. He made the All-Star team his rookie year, but his fast start tailed off and he ended up hitting .257 with 10 home runs and 58 RBIs that season. Those numbers would remain consistent, and the Cubs traded Fukudome to the Indians in July for a couple of minor leaguers. Between the teams, he hit .262 with eight homers and 35 RBIs last season.
The White Sox views Fukudome as a left-handed hitter who can play center and right.
"We're not looking for this guy to come in and completely change his approach," Hahn said. "We just want him to be the player he's proven to be over the last four years."
The White Sox have been pretty quiet on the free-agent front this offseason, the first after manager Ozzie Guillen left for the Marlins and was replaced by Ventura. Left-hander Scott Olsen and outfielder Delwyn Young are the highest profile signings.
Information from The Associated Press was used in this report.