Upshaw, 6 feet 2, 272 pounds, spent the past two seasons with the Atlanta Falcons after four seasons with the Ravens, who drafted him out of Alabama in 2012.
He has seven career sacks, five forced fumbles, five fumble recoveries and 215 tackles in 90 career games, 56 of them starts.
Upshaw entered the league as a linebacker and played there for the Ravens while helping them win the Super Bowl in February 2013 by forcing a fumble that led to a touchdown drive.
He signed with Atlanta in 2016 after visiting with the Jets. The Falcons moved him to defensive line and he played in the Super Bowl that season, coming up with a sack in the overtime loss to the New England Patriots.
To make room on the roster Thursday, the Jets waived defensive lineman Chris Jones, who was signed on June 5.