The deal is pending a physical.
In an effort to free up some salary for Bradley, the Cubs are expected on Tuesday to finalize a deal to send Jason Marquis to the Colorado Rockies in exchange for reliever Luis Vizcaino, MLB.com reported Monday.
Adding Bradley was one of the top priorities this offseason for the Cubs, who got swept out of the playoffs for the second straight year after a lineup loaded with right-handers struggled against the Los Angeles Dodgers.
A switch-hitter, Bradley batted .321 with 22 homers for the Texas Rangers while leading the American League with a .436 on-base percentage. He made the All-Star team while serving primarily as the designated hitter.
Playing with the Expos, Indians, Dodgers, Athletics, Padres and Rangers in a nine-year career, Bradley has batted .280 with 103 home runs and 399 RBIs. Injuries have allowed him to surpass 400 at-bats in a season only twice in his career.
In Chicago, he'll fill the Cubs' need for a left-handed bat in the middle of the order and will be used mostly in right field even though he has played 100 games in the field just once -- in 2004 with the Dodgers. The Cubs will likely spell him with Kosuke Fukudome, who will also platoon with Reed Johnson in center. Fukudome was in right field last season.
Chicago general manager Jim Hendry declined comment.
The Cubs led the National League with 855 runs during the regular season before the Dodgers outscored them 20-6 in the playoffs. It was no secret they wanted to balance their batting order, and Bradley should complement right-handed sluggers such as Alfonso Soriano, Derrek Lee and Aramis Ramirez.
Now the Cubs have added Bradley to the mix, hoping he can help them advance in the postseason and, ultimately, win their first championship since 1908. But they're taking a calculated gamble.
They will be the seventh team for Bradley, who has a history of behavioral issues.
He slammed a plastic bottle at the feet of a fan in the right-field seats at Dodger Stadium in 2004 after someone threw it on the field, drawing a five-game suspension. With San Diego in the pennant chase in 2007, he tore the ACL in his right knee when he was spun to the ground by Padres manager Bud Black, who was trying to keep him from umpire Mike Winters. Bradley claimed he was baited by Winters, who was suspended the final five days of the regular season and didn't work the postseason.
Bradley also got a four-game suspension for tossing a bag of balls onto the field after an ejection. And when he was with Cleveland, he had a dugout confrontation with Indians manager Eric Wedge during spring training in 2004 before getting traded to Los Angeles.
Information from The Associated Press was used in this report.