The contract includes a second-year player option that, if rejected, turns into a team option, sources said.
Gardner, 37, became a free agent in November when New York declined his 2021 club option. He has been with the Yankees since 2008 and is their last player from the 2009 World Series champions. His 13-year tenure with one team during his career was tied for fifth among active players.
Gardner hit .223 with five homers and 15 RBIs in the shortened season, down from .251 with career highs of 28 homers and 74 RBIs in 2019. The Yankees agreed to a deal with a $2 million signing bonus and an $8 million salary for 2020, which became $2,962,963 in prorated pay.
He lost playing time in 2020 to Clint Frazier, who hit .267 with eight homers and 26 RBIs.
Drafted in the third round by the Yankees in 2005, Gardner was the longest-tenured member of the team, having spent his entire 13-year big league career in the Bronx. He has a .259 average, 129 homers and 539 RBIs.