The Dolphins elevated Cook from the practice squad to the active roster Saturday.
The Dolphins placed Willis (abdomen) on injured reserve Tuesday, so Cook will operate as the team's backup quarterback behind Kyle McCord for Sunday's game against the Colts. Cook appeared in five regular-season games (four starts) for the Jets in 2025, when he completed 57.5 percent of his passes for 739 yards, two touchdowns and seven interceptions while rushing for 49 yards on 13 carries.