The move comes on the heels of the Seahawks signing Stephen Morris last week, one day after reports surfaced that the team postponed a scheduled workout with former San Francisco 49ers quarterback Colin Kaepernick.
Kaepernick's workout was scratched due to conflicting reports, with ESPN saying that Seattle wanted him to commit to standing for the national anthem. However, the NFL Network reported that Kaepernick's stance on the national anthem was not the reason the workout was postponed.
Davis did not throw a pass in his three games last season. He has experience with new Seahawks offensive coordinator Brian Schottenheimer, having played for him with the then-St. Louis Rams.
The 28-year-old Davis made eight starts for the Rams in 2014, one of which was a win over the Seahawks.
Also on Monday, the Seahawks signed three exclusive rights free agents: center Joey Hunt, defensive end Branden Jackson and long snapper Tyler Ott.
Linebacker Paul Dawson also signed a one-year contract after recording three tackles in three games last season.
Hunt, who was a sixth-round pick in the 2016 NFL Draft, started one game in his rookie season before spending the majority of the 2017 campaign on the practice squad.
Jackson collected two tackles in 12 games in 2017.
Ott played in all 16 games last season.