The White Sox non-tendered De Los Santos on Friday.
The White Sox claimed De Los Santos off waivers Saturday.
The Yankees designated De Los Santos for assignment Wednesday.
The Yankees acquired De Los Santos and right-hander Thomas Balboni from the Padres in exchange for outfielder Brandon Lockridge on Thursday.
De Los Santos registered a hold against Atlanta on Friday, striking out one batter over a perfect two-thirds of an inning.
De Los Santos signed a one-year contract with the Padres on Thursday to avoid arbitration.
De Los Santos (5-2) struck out the only batter he faced and earned the win in Game 2 of Friday's doubleheader versus the Tigers.
De Los Santos (3-1) struck out one without giving up a hit or a walk in a scoreless inning to earn the extra-inning win over the Athletics on Tuesday.
De Los Santos (2-1) allowed four runs on two hits and two walks without recording an out to take the loss Tuesday versus the Red Sox.
De Los Santos (2-0) earned the win Monday over the Yankees, recording two outs without allowing a baserunner.