The 31-year-old Jackson was just 16-34 with a 5.58 ERA in two seasons with Chicago after signing a four-year, $52 million contract after the 2012 season.
Jackson is still owed about $15.6 million through the 2016 season, on the assumption he clears waivers. The Cubs have 10 days to trade, waive or give Jackson his outright release.
"I want it to be known what a professional athlete and person Edwin is," Cubs manager Joe Maddon said. "The word 'class' is thrown out there way too readily, too easily. I really believe it applies to him."
This season, Jackson has made 23 appearances out of the bullpen, striking out 23 batters in 31 innings.
"I wasn't really expecting it," Jackson said, according to MLB.com. "At this point in my career, it's hard for me to say I'm surprised about anything that happens.
"It [stinks] but it's the business part of the game," he added. "I'll be all right, the team will be all right. Hopefully in my time here, I left some kind of positive influence on some of the guys. They can continue to keep it going and proceed to go ahead and prosper in the game."
Chicago signed Soriano last month to a minor league deal, and he is set to join the team before Monday’s game against the Cincinnati Reds. Chicago enters the series at 49-41, eight games behind the St. Louis Cardinals in the NL Central.
Both Soriano and Jackson played for Maddon in Tampa Bay.
Soriano saved 32 games last season for the Washington Nationals, but also blew seven save opportunities. He has a career 2.85 ERA with 207 saves.
- Scooby Axson