The terms of the deal have not yet been disclosed.
Rodney, 38, is a two-time MLB All Star. He is just two seasons removed from posting a 2.85 ERA with the Seattle Mariners and leading the American League in saves with 48.
His 2015 season was not as successful, however, as he recorded a 4.74 ERA with seven blown saves in 68 appearances for the Mariners and Cubs combined after being designated for assignment and later acquired by Chicago in August.
Rodney was the AL Comeback Player of the Year in 2012, as well as the MLB Delivery Man of the Year.
He has a career 3.71 ERA with 236 saves and 685 strikeouts.