Bears general manager Ryan Pace announced the hiring on Monday. Nagy is the 16th coach in franchise history.
The 39-year-old entered the NFL ranks in 2008 as a coaching intern with the Philadelphia Eagles. He was a coaches assistant and worked in offensive quality control for the Eagles, before joining the Kansas City Chiefs in 2013 as a quarterbacks coach. He became the Chiefs' offensive coordinator this season.
Kansas City ranked No. 5 in total offense, No. 6 in points per game, No. 7 in passing yards and No. 9 in rushing this season. The Chiefs had just eight giveaways, the fewest in the NFL.
Nagy completed 65.5 percent of his throws for 18,866 yards and 374 touchdowns in six seasons in the Arena Football League. He played for the New York Dragons, Carolina Cobras, Georgia Force and Columbus Destroyers. He played collegially at Delaware.
Before joining the NFL coaching circle, Nagy was an assistant coach at Manheim Central High School and quarterbacks coach at Cedar Crest High School. He was the offensive coordinator at Palmyra Area High School in 2008 and 2009.
The Bears will hold an introductory press conference with Nagy on Tuesday at Halas Hall.