The All-Star reliever agreed to a $15 million, three-year contract Sunday that adds two years and $12 million to his previous deal.
The 34-year-old Thornton went 5-4 with a 2.67 ERA and a career-high eight saves last season. He fanned 81 in 60 2-3 innings to become the first White Sox reliever to lead the AL in strikeouts since Keith Foulke in 1999.
"It was an easy choice with an organization like this, with what they've done the last five months or so, retaining the core guys, adding the pieces and expecting to win," Thornton said.
The 6-foot-6, 235-pound Thornton gets $3 million this season, the salary called for in the option year of his previous contract, which was exercised in October. His new contract adds salaries of $5.5 million each in 2012 and 2013 plus a $6 million club option for 2014 with a $1 million buyout.
Manager Ozzie Guillen hasn't chosen who will be Bobby Jenks' replacement as the closer, but indicated at times during the offseason that he would prefer Thornton in the role.
While he has made it clear he would like to be go-to guy in the ninth inning, Thornton knows the decision is not up to him.
"I've made that clear that I will do what they want, even before the deal," he said. "They gave me security and trust me. My goal is to stay in Chicago the rest of my career."
Jenks signed a two-year, $12 million deal with the Boston Red Sox this offseason. Offering Thornton a similar contract might be the final jab the White Sox front office throws in a feud that Red Sox manager Terry Francona recently helped quell.
Thornton is the White Sox all-time leader with 100 holds and ranks fifth with 336 relief appearances.