Johnson said by text message he would sign the contract next week.
Running back Jamaal Charles signed a one-day contract with the team on Wednesday so he could retire as a Chief.
Johnson, 36, was the Chiefs' first-round draft pick in 2005 from Texas. He played 13 seasons with the team and was one of the NFL's top linebackers for much of that time.
Johnson was selected to play in the Pro Bowl four times and was a first-team All-Pro in 2011. Johnson has 27.5 sacks and 14 interceptions for the Chiefs.
The Chiefs released Johnson last March. He signed with the Oakland Raiders but lasted just six games before the Raiders released him.