The deal includes a team option for the 2022 season. Terms were not disclosed.
"Tucker has made us proud on the field with his play and off the field with his community involvement," Reds general manager Dick Williams said in a statement.
The switch-hitting Barnhart, who would have been eligible for salary arbitration after this season, is hitting .272 with six home runs and 42 RBIs. Defensively, he only has one error this season and leads all National League catchers by throwing out 44 percent of baserunners attempting to steal.
"He worked his way up through our system, improving every step of the way, and has established himself as an elite defensive catcher and a productive offensive player," Williams said. "Switch hitting catchers who can impact the game defensively are tough to find."