Jenks, an American right-hander, died on Friday in Sintra, Portugal, where he had been battling adenocarcinoma, a form of stomach cancer, the White Sox said in a statement.
"We have lost an iconic member of the White Sox family today," said White Sox chairman Jerry Reinsdorf.
"He and his family knew cancer would be his toughest battle and he will be missed as a husband, father, friend and teammate. He will forever hold a special place in all our hearts."
Jenks made saves in games one and four of the 2005 World Series, in which the White Sox swept Houston in four games. The rookie also pitched scoreless 11th and 12th innings in a 14-inning Chicago win in game three.
He threw the final pitch of the World Series in game four as the White Sox ended an 88-year title drought.
"None of us will ever forget that ninth inning of game four in Houston, all that Bobby did for the 2005 World Series champions and for the entire Sox organization during his time in Chicago," Reinsdorf said.
Jenks, an American League All-Star selection in 2006 and 2007, pitched for the White Sox for six MLB seasons from 2005-10, going 14-18 with a 3.40 earned-run average, 173 saves and 334 strikeouts over 329 relief appearances.
In 2006 and 2007, Jenks recorded back-to-back 40-save seasons, which made him the second-youngest to achieve the feat at the time. Jenks retired 41 batters in a row in 2007 to match what was then an MLB record.
Jenks finished his career in 2011 with the Boston Red Sox, playing only 19 games due to bone spurs on his spine that hampered nearby nerves and tendons.
Overall, Jenks went 16-20 with a 3.53 ERA, 173 saves and 351 strikeouts over 348 career games.
