McDermott will take on the role of scouting upcoming opposition as part of Rodgers' technical team alongside assistant manager Dean Austin and football consultant Frank Lampard Snr, while Gibbs will take control of the Royals' reserves.
Rodgers told the club's official website: "Brian McDermott has done a great job as chief scout and reserve team manager and he will now become a member of my technical team with special responsibility for our opponents.
"You have to understand your opponents and how they operate and Brian has great experience at this level and above.
"Nigel Gibbs will then take sole control of the reserve team. The development group is very, very important and this allows him freedom in the role."