Rodney was designated for assignment by the Mariners last week, giving the team 10 days to trade or release him.
Rodney pitched 50 2/3 innings for the Mariners this season and had a 5.68 ERA. He blew six of his 22 save opportunities and posted a 1.50 WHIP, his worst since 2011. He led the majors with 48 saves last season.
The trade reunites Rodney with manager Joe Maddon, his boss in 2012 and 2013 with the Tampa Bay Rays. The Cubs previously acquired former Rays closer Rafael Soriano, who is currently injured.
Rodney, 38, is the final year of his contract.
- Dan Gartland