Lee was a 2016 first-round pick by the Jets, taken 20th overall, and played three underwhelming seasons in Gotham.
Across three years, he played in 40 games (36 starts) with 238 tackles (79.3 per season).
Lee, who was suspended four games in 2018 for violating the league's substance-abuse policy, will get a new start in Kansas City, which is looking to revamp its defense after a slew of offseason departures.
The move is also a somewhat interesting one considering reports Wednesday that cited disagreements between Gase and Maccagnan surrounded the free-agent acquisitions and the price tags for linebacker C.J. Mosely and running back Le'Veon Bell.