The person says the agreement includes a club option for a third year. The person spoke on condition of anonymity because the deal has not been announced.
The 38-year-old right-hander will fill a setup role for closer Craig Kimbrel. He will help replace Jordan Walden, who was traded with right fielder Jason Heyward to the Cardinals in the offseason deal that sent starting pitcher Shelby Miller to Atlanta.
Grilli was an All-Star closer for the Pirates in 2013, when he had 33 saves. He lost his stopper job before he was traded to the Angels on June 27, 2014. He finished with a combined 12 saves and 4.00 ERA last season.