A source familiar with the deal told ESPN's Jeff Passan that the contract is for $7.5 million.
The move comes a day after the A's decided not to tender a contract to another member of the team's bullpen, reliever Blake Treinen, making him a free agent. Treinen, a right-hander, posted a 0.78 ERA and saved 38 games as the A's closer in 2018 but his ERA rose to 4.91 in 2019 as he lost his closer's job to Liam Hendriks.
Diekman, 32, was acquired by the A's in a trade with the Kansas City Royals in July. He became a free agent after the season.
After joining Oakland, he went 1-1 with a 4.43 ERA in 28 appearances. The eight-year veteran has a 3.90 ERA in his career in 441 appearances for five major league teams.