This move creates a roster spot for Matt Moore, who is reportedly signing a one-year contract with the Chiefs.
Patterson, 23, wound up going undrafted out of Michigan back in May before signing on with the Chiefs. He was a two-year starter at Michigan and a third-team All-Big Ten selection as a senior.
During his college career at Ole Miss and Michigan, Patterson completed 60.3 percent of his passes for 8,800 yards, 68 touchdowns and 27 interceptions over the course of four seasons and 36 games.
Patterson also rushed for 476 yards and eight touchdowns.