Flynn guided Rovers to the League One title following a dramatic injury-time victory at fellow promotion hopefuls Brentford last Saturday.
The 57-year-old was appointed Rovers boss in early January after Dean Saunders left to take over at Wolves.
Doncaster have already started their search to fill the vacancy as they prepare for a return to the Championship.
A statement from Doncaster 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.
"Brian will go down in history following the dramatic end to the season and the club see Brian as the ideal man to lead the development of Doncaster Rovers as a force both at senior and youth level."