The Bucs are last in the league with four sacks through five games.
Magee was obtained Tuesday in exchange for an undisclosed pick in the 2011 draft. The Bucs also will receive an undisclosed pick in the deal.
Magee was a third-round pick by the Chiefs in 2009.
The second-year pro appeared in 17 games for Kansas City, including one start. The former Purdue standout has two career sacks.
To make room on the roster, the Bucs placed backup running back Kareem Huggins on injured reserve. Huggins hurt his right knee during Sunday's 31-6 loss to New Orleans.