The Yankees, who will pay $1.6 million of Sax's $10.9 million contract, also got right-handers Robert Wickman and Domingo Jean. The trade unites the 25-year-old Perez with his older brother Pascual.
The deal, almost identical to one the Yankees backed out of a week ago, is the team's third major player transaction of the week. Earlier, New York signed free agents Danny Tartabull and Mike Gallego.
Sax, who will be 32 on Jan. 29, was the only Yankee regular to bat over .300 last season. The 1982 National League Rookie of the Year for the Los Angeles Dodgers, Sax was Called "one of the finest offensive second basemen in the game" by White Sox general manager Ron Schueler.
"It is not very often that you can pick up an All-Star, so we're very pleased with acquisition of Steve Sax," Schueler said. "The Chicago fans will appreciate his fire, determination and style of play."
Yankees general manager Gene Michael praised Sax, who hit .304 with a career-high 10 homers, 56 RBIs and 31 stolen bases last season, but said the club needed to fortify its pitching staff.
"In return,we are getting a good pitcher in Melido Perez, working mostly out of the bullpen for the first time, was 8-7 with one save and a 3.12 earned run average for the White Sox last year. He is 45-46 over four seasons with a career ERA if 4.26.
Although he figures to join the rotation, Melido Perez did his best work out of the bullpen last season. After moving there May 29, he was 7-3 with a 2.22 ERA.
In 1990, Perez pitched a six-inning, 8-0 no-hit victory over the Yankees.
Wickman 22, was 5-1 with a 2.05 ERA at Claa A Sarasota and 6-10 with a 3.56 ERA at AA Birmingham. He was Chicago's second-round selection in the June 1990 draft.
The 23-year-old Jean was 12-8 with a 3.30 ERA at Class A South Bend. He allowed 121 hits and 66 walks while striking out 141 batters in 158 innings.