Ely was dominant at Class AA Birmingham last season with a 14-2 record and a 2.82 earned-run average. He also led the Southern League with 125 strikeouts.
The White Sox drafted Ely out of Miami (Ohio) in the first round of the 2007 draft. He went 28-7 in three seasons at Miami.
The Dodgers will choose two of three prospects the White Sox offered in the trade sometime before the first of the year, according to a Major League Baseball official with knowledge of the deal.
The White Sox received Pierre and cash toward his $18.5 million, two-year contract. The White Sox are only obligated to pay Pierre $3 million in 2010 and $5 million in 2011.