Adams gets a $1 million buyout and becomes a free agent following Friday's decision.
The 31-year-old hit .226 with 20 homers and 56 RBIs in 111 games during the regular season.
He had just four plate appearances in the postseason and his only World Series action was a walk as a pinch hitter in Game 3. His pinch single off Adam Wainwright sparked a two-run rally in Game 2 of the NL Championship Series.
Adams, 31, is an eight-year big league veteran with St. Louis (2012-17, '18), Atlanta (2017) and Washington (2018, '19).