Reid was fired as the coach of the Philadelphia Eagle Dec. 31 and officially joined the Chiefs late last week.
Sutton, who turns 62 this month, had been with the New York Jets in various capacities on the defensive staff since 2000. Last season he was in charge of the team's linebackers and also assistant head coach.
New York had granted Reid permission to interview Sutton.
Pedersen, 44, was on Reid's staff in Philadelphia, including serving as quarterbacks coach the last two seasons. He played quarterback in the NFL for 12 seasons.
"Bob is a creative coach that is going to give our defense a variety of looks and packages," said Reid. "He has a lot of experience and is well respected across the league. Bob has a high football IQ and knows how to get the most out of his players.
"Doug has been around the game a long time and he has great vision," Reid said. "As a former player in this league, he sees the game from a different perspective, and that will be a great benefit for our players. He has a knack for developing talent, and he's a good communicator. Doug is ready for this position."