The Midlanders, who appointed Super Bowl legend Tom Brady to the club's advisory board in August, have opted to change their boss by parting company with John Eustace.
The Championship side have turned their attention to Rooney, who recently resigned from his post with Major League Soccer side DC United.
Rooney becomes their new manager, on a three-and-a-half year contract, with former Reds team-mate O'Shea and ex-England defender Ashley Cole joining his coaching staff.
United's all-time record goalscorer has already experienced Birmingham's current level, having been Derby County's boss between 2021 and 2022.