The Redskins also signed defensive end Marcus Smith, guard Zac Kerin and center Demetrius Rhaney while placing cornerback Quinton Dunbar, wide receiver Trey Quinn and guard Jonathan Cooper on injured reserve.
The move for Johnson was necessitated after quarterback Colt McCoy sustained a fractured right fibula during the final play of the first quarter of Monday's 28-13 setback to the Philadelphia Eagles. McCoy previously replaced Alex Smith, who is out for the season with a broken leg.
"Oh, he's been discussed for sure and right now at this point, we already had a workout last week for the few guys," Gruden said. "We had a couple other guys come in today and then it's just going to be a matter of which way we want to go. Do we want to go with a guy that's familiar with my terminology who we worked out last week, or with a new guy to back up (Mark) Sanchez with a similar skill set, or go with a guy and teach basically a whole new kind of offense with a new offensive line and with a lot of those zone reads and all that stuff.
"Not a lot of time to really get a brand new quarterback and new system installed and taught in a couple of days of practice. He's been talked about and discussed, but we'll probably go a different direction."
Kaepernick has not played in the NFL since 2016, when he began kneeling during the national anthem to protest racial injustice. The 31-year-old Kaepernick has filed a collusion suit against the the league, arguing that owners have colluded to keep him off any NFL roster since he hit free agency in 2017.
Johnson had been on the roster of the San Diego Fleet in the Alliance of American Football, but was released from that contract in order to return to the NFL. He will serve as the backup to Sanchez, who completed 13 of 21 passes for 100 yards in the loss to the Eagles.
The 32-year-old Johnson has played 29 NFL games with the Tampa Bay Buccaneers, Cleveland Browns and Cincinnati Bengals. He was a fifth-round pick of the Buccaneers in the 2008 NFL Draft, which marked the final year in Tampa Bay for Gruden.
The Redskins (6-6) will look to end a three-game slide on Sunday (1 p.m.) against the visiting New York Giants (4-8).