Graveman's new deal is for $1.25 million and includes performance bonuses, according to Jon Heyman of MLB Network.
The Mariners declined the hurler's $3.5-million option for 2021 on Wednesday.
Graveman made two starts for Seattle this season but then missed 27 games with a neck spasm. The 29-year-old pitched out of the bullpen when he returned and posted a 3.60 ERA over 10 innings. He owns a career 4.44 ERA over six campaigns with the Mariners, Oakland Athletics, and Toronto Blue Jays.