The person spoke to The Associated Press on condition of anonymity Tuesday because the team had not yet announced the deal.
Nady's contract is contingent on him passing a physical. He underwent elbow reconstructive surgery for the second time in his career last July while with the New York Yankees. He played in only seven games.
Nady joins a Cubs outfield mix that includes Alfonso Soriano, Kosuke Fukudome and Marlon Byrd. Nady is a career .280 hitter with 87 homers in 679 major league games with the Padres, Mets, Pirates and Yankees.
In addition to the base salary, Nady could earn another $2.05 million in performance bonuses based on games played.
AP Sports Writer Ronald Blum contributed to this report.