The 26-year-old was 17-8 with a 3.84 ERA for the White Sox last year and is 25-18 in 73 games over parts of five big league seasons with the Philadelphia Phillies and White Sox.
Floyd will make $750,000 this year, $2.75 million in 2010, $5 million in 2011 and $7 million in 2012, and the White Sox hold a $9.5 million option for 2013.
Floyd had been set to make $520,000 this year under a one-year deal agreed to Feb. 25. He would have been eligible for arbitration after this season and for free agency following the 2012 season.
"We wanted to wait until we got in spring training to take another look where we are, assess where we are in the present and where we want to be in the future," Williams said. "We wanted to make overtures to a number of people that we felt were going to be a part of our next core, which we have done in years past with the [Jon] Garlands, the [Mark] Buehrles. We're starting the process once again."
Chicago also traded minor league catcher Chris Stewart to the New York Yankees for future considerations. The 27-year-old had been in the Yankees organization before signing a minor league deal with the White Sox and .279 with two homers at Triple-A Scranton-Wilkes Barre last season.