Although Kotsay is not the player he was three years ago, he can supply the Sox with insurance at all three outfield positions as well as first base.
Kotsay was designated for assignment last week, which means the Red Sox had 10 days to trade him or give the player his unconditional release.
In the deal, the White Sox received money to cover what Boston owed to Kotsay.
According to sources close to the trade, the Red Sox will send the White Sox close to $390,000 to cover the rest of Kotsay's contract.
Brian Anderson had four good shots to make the team as a regular but never hit well enough to hold on to a job. Anderson's worth is as a defensive specialist and a team's decent fourth outfielder.
The White Sox's 2007 first-round pick will be missed in the clubhouse by his teammates, but not by manager Ozzie Guillen and the Sox's coaching staff, who felt Anderson underachieved.
Major League Baseball players have 72 hours to report after a trade. According to team sources, a roster move will not be made today. The likelihood is Kotsay will show up to the team in Minnesota on Wednesday.