Flynn had guided Rovers to the League One title last weekend to earn his side promotion to the Championship.
However, the 57-year-old soon signalled his wish to return to heading the development of players at the club.
A club statement read: "Following the end of the season, Brian Flynn has approached the club and expressed a desire to return back to what he sees as his passion in the development and recruitment of players.
"In line with this, the owners have offered Brian a senior role within the club developing and supporting whoever is to manage the side as it goes into the Championship.
"Brian will be involved in the search for a new manager and new players for the challenge ahead in one of the most competitive leagues in the world."
Flynn had taken charge of Doncaster after Dean Saunders left the club to join Wolverhampton Wanderers.