ESPN The Magazine's Buster Olney first reported the deal.
The Padres had talked about not re-signing Correia, who went 12-11 with a 3.91 ERA in 33 starts last year.
Correia, 29, joined San Diego last season after spending his first six in San Francisco. He was taken by the Giants in the fourth round of the 2002 draft.
Correia had a $750,000 base salary last season and earned $350,000 in performance bonuses based on starts.
Information from The Associated Press contributed to this report.