The White Sox said Jenks died Friday in Sintra, Portugal, where he was being treated for adenocarcinoma, a form of stomach cancer.
Jenks helped the White Sox win the 2005 World Series, saving four games in six appearances during the postseason. He was an All-Star in each of the next two seasons while saving 41 games in 2006 and 40 in 2007.
Ozzie Guillén, who managed that World Series-winning squad, had a signature move to summon Jenks from the bullpen, throwing his arms wide open to show that he wanted the 6-foot-4, 275-pound closer. Jenks died weeks before the White Sox were set to hold a 20th anniversary reunion for the franchise's most recent title-winning team.
"Everyone remembers the moment when I called for the big fella in the World Series," Guillén said in a statement. "Everyone has a favorite story about Bobby, so the 2005 reunion will be a great opportunity to get together with all his teammates and coaches and relive some of our greatest memories of him."
Jenks retired 41 consecutive batters in 2007, matching a record for a reliever.
"He was embarrassing guys, good hitters, right away," former White Sox first baseman Paul Konerko said in a video tribute.
Jenks saved 173 games for the White Sox from 2005-10 before finishing his career with 19 appearances in 2011 for the Boston Red Sox. For his career, he was 16-20 with a 3.53 ERA and 351 strikeouts in 348 appearances, all in relief.
"He and his family knew cancer would be his toughest battle, and he will be missed as a husband, father, friend and teammate," White Sox owner Jerry Reinsdorf said. "He will forever hold a special place in all our hearts."
Jenks is survived by his wife, Eleni Tzitzivacos, their two children, Zeno and Kate, and his four children from a prior marriage, Cuma, Nolan, Rylan and Jackson.
"As a teammate," former White Sox outfielder Aaron Rowand said, "he was the best."