Bailey will receive a two-year, $10.5 million deal, according to a PFT source. He is scheduled to get $6 million this year with $3.5 million guaranteed.
The defensive lineman also visited the Patriots, Panthers and Seahawks this offseason.
The Chiefs made Bailey a third-round pick in 2011, and he had spent his entire career with Kansas City. He started most of the past five seasons, including 15 starts last season across the regular season and playoffs.
Bailey had 38 tackles, six sacks and two forced fumbles in the regular season and made five tackles in the AFC Championship Game.