De Los Santos, who will wear uniform number No. 66, has no major-league experience. He was acquired from the Tampa Bay Rays on September 13, 2013 in exchange for cash considerations.
He is 35-40 with a 3.96 ERA (276 ER/627.0 IP), nine saves and 416 strikeouts in 201 career appearances (85 starts) over eight minor league seasons between the Rays (2007-13) and White Sox (2013-14) organizations.
Eaton, 25, left last night's game in the fourth inning after going 0-2 with a walk. He is hitting .276 (27-98) with five doubles, a triple, home run, 14 RBI and 20 runs scored over 25 games this season, his first with the White Sox. He is tied for seventh in the American League in runs scored.
Sierra, 25, was designated for assignment by the Blue Jays on May 1 after going 2-34 (.059) with two RBI and two runs scored over 34 games this season.
The 6-foot-1, 220-pound Sierra batted .290 (31-107) with 13 doubles, a triple, home run, 13 RBI and 11 runs scored over 35 games in 2013. He hit .315 (23-73) with 10 RBI vs. right-handers and .429 (9-21) with RISP.
Sierra hit .317 (26-82) with 12 doubles, a homer and 11 RBI over 25 games in September last season. He ranked among the AL September leaders in doubles (3rd), extra-base hits (T4th, 14), slugging percentage (8th, .524) and on-base percentage (9th, .385).
He is a career .229 hitter (66-288) with seven home runs and 30 RBI in 97 games over three seasons with Toronto (2012-14). He has appeared in 74 games (66 starts) in right field and four (three) in left.
He was signed by Toronto as a non-drafted free agent on December 20, 2005.
Jones, 28, has not pitched in a game this season after being placed on the disabled list on April 4.
The White Sox 40-man roster is at 40.