Jones agreed to a $500,000, one-year contract with Chicago on Wednesday.
Earlier in the week, infielder Omar Vizquel also signed a one-year deal with the White Sox.
Jones hit .214 with 17 homers and 43 RBIs in 82 games with Texas this year while making 53 starts as the designated hitter, 12 in left field, five in right field and four at first base.
This is an opportunity to add a power bat to the roster while improving our outfield depth," White Sox general manager Kenny Williams said. "With the addition of Andruw, Mark Kotsay and Omar Vizquel, we feel our bench is taking shape to be a strong asset heading into the 2010 season."
Vizquel, a 42-year-old infielder, agreed Monday to a one-year deal. Earlier, the White Sox re-signed Kotsay, another utility player who can play the infield and outfield.