The lead coach of the under-23s was appointed by Lee.
Lee is the new boss of Hartlepool.
Lee began his career with Pools and made over 200 league appearances before joining Wednesday.
He has left his position as the under-23s coach at Middlesbrough to take over at the League Two side.
Lee's first game in charge will be Saturday's trip to Lincoln City.
He will be assisted by Michael Nelson.
Raj Singh told the club website that they always wanted to appoint a manager and coaching team that was modern in their approach, with the ability to build on the foundations that have been put in place.
We believe that we have two very forward thinking coaches that are also strong and capable characters to lead the players and club forward, and that is why we haveGraeme and Michael Nelson as our coaches.
"Michael and Graeme have a deep connection with our club having played nearly 500 games for us, they are natural leaders and have captained various sides in the Football league, they know this level of football remarkably well."
After leading the Victoria Park side back to League Two, he left to take over at National League Stockport.
Tony Sweeney will be taking charge of the team for the last time when they play Wednesday in the EFL Trophy.
