The team announced the signing and sent Pennington to Triple-A Scranton/Wilkes-Barre to get playing time, and he is expected to join the roster soon.
Friday, he played for the RailRiders and went 1-for-3 against the Buffalo Bisons.
Overall the Yankees have 11 players on the injured list.
The veteran brings plenty of Major League experience to the team, as he has appeared in 971 games over 11 seasons with the Oakland Athletics (2008-12), Arizona Diamondbacks (2013-15), Toronto Blue Jays (2015), Los Angeles Angels (2016-17) and Cincinnati Reds (2018).
He has started 741 games in his Major League career, with 544 of those starts coming at the shortstop position.
Pennington was with the Oakland Athletics this spring, and was cut after playing in 17 Cactus League games, hitting .296.
After losing shortstop Troy Tulowitzki earlier in the week to injury, the Yankees brought up 23-year-old Thairo Estrada from Triple-A to give them some infield depth.
For now, Gleyber Torres is expected to get most of the playing time at shortstop for the Yankees.