Chicago received right-hander A.J. Puckett and left-hander Andre Davis from Kansas City.
The Royals also received cash considerations in the deal. Cabrera is making $15 million this season and will become a free agent after this season.
Davis is the 13th-ranked player in the Royals’ farm system, while Puckett is No. 22, according to MLB.com.
Cabrera, 32, is hitting .295 with 13 home runs and 56 RBIs in 98 games (428 plate appearances).
The Royals entered Sunday’s game with a 54-48 record and are in second place in the AL Central, three games behind the division-leading Cleveland Indians.
Kansas City holds the second wild-card spot by 2½ games over Tampa Bay. The Royals had their season-high nine-game winning streak snapped by Boston on Saturday night — 9-8 in 10 innings.
The trade marks a return to Kansas City for Cabrera, who also played for the Royals in 2011. That season he set career bests in hits (201) and RBIs (87).
Davis, 23, is 5-4 with a 4.83 ERA in 18 starts for Lexington, the Royals’ Class A team in the South Atlantic League. Puckett, 22, is 9-7 with a 3.90 ERA in 20 starts for Wilmington, the Royals’ advanced Class A team in the Carolina League.
In 13 major league seasons, Cabrera has a .286 average, 127 home runs and 739 RBIs in 1,618 games for the Yankees, Blue Jays, Royals, Giants, Braves and White Sox.
The Associated Press contributed to this report.