Soriano, 35, signed a minor-league contract with the Cubs in June and did not allow an earned run in seven games in the minors this year. Maddon said last week that he was told Soriano’s fastball reached 94 mph in his most recent outings.
Soriano was an All-Star with the Tampa Bay Rays in 2010, when he led the American League with 45 saves. He had a 1.73 ERA in 62 1/3 innings and a 0.802 WHIP. He finished eighth in Cy Young voting and 12th in MVP balloting.
Soriano will be reunited with Maddon, his old Rays manager, in Chicago.
After his stellar 2010 season, Soriano signed a three-year, $35 million contract with the New York Yankees. He opted out of the deal with one year remaining and signed a two-year, $28 million deal with the Washington Nationals.
Soriano blew a career-high seven saves in 2014 and did not find a new team that winter.
Jackson, who is in the third year of a four-year contract he signed with the Cubs in 2012, is due to make $13 million next season. The Cubs will have 10 days to trade or release him.
Jackson had a 6.33 ERA in 28 games last season as a starter and transitioned to a long relief role this season, improving his ERA to 3.19. His WHIP also fell from 1.642 to 1.355.
- Dan Gartland