MLB.com reports that the deal, which is pending a physical, could be worth up to $15 million.
Fiers, 33, is coming off his best season (12-8, 3.56 ERA) as a major league starter, helping Oakland to an unlikely postseason berth after being acquired in August.
With an expected arbitration number of around $10 million, the A’s had initially not tendered Fiers a contract, making him a free agent.
Fiers bounced around from Milwaukee to Houston and then Detroit before landing in Oakland. His career ERA of 4.04 and 8.3 strikeouts per 9 innings are both respectable, and he has earned a reputation as a solid back-of-the-rotation starter.