Gardner's deal includes an option for a second year worth $10 million, reports MLB.com's Bryan Hoch.
The veteran will actually receive $10 million guaranteed in 2020 ($8 million in salary and a $2-million signing bonus) and has a $2.5-million buyout attached to his 2021 club option, according to Joel Sherman of the New York Post.
Gardner is expected to start in center field for the Yankees while Aaron Hicks recovers from Tommy John surgery.
The 36-year-old had a career year in 2019, hitting .251/.325/.503 with 28 home runs, 26 doubles, and 74 RBIs in 141 games.
Defensively, he recorded a plus-5 in defensive runs saved in the outfield last season, though his DRS was a minus-2 in center.
Gardner has spent every season of his 12-year career with the Yankees.
During that time, he's appeared in 1,499 games, batting .260/.342/.401 with 124 home runs, 524 RBIs, and 267 steals.
He won a World Series with the Yankees in 2009 and was an All-Star in 2015.