The League Two side have been without a permanent manager since the beginning of November when Dave Challinor left his role at the club.
Lee made over 200 appearances for Hartlepool as a player before going on to have spells at Wednesday, Doncaster Rovers and Bradford City.
For Doncaster, Lee scored the winning goal in their 3–2 win over Bristol Rovers in the 2007 Football League Trophy final at the Millennium Stadium in Cardiff.
He has left his role as manager of Middlesbrough Under-23s to take up the top job at Pools.
The 43-year-old will not be in the dugout in South Yorkshire tonight, as Hartlepool face the Owls in the Papa John's Trophy. Tony Sweeney will remain in charge.
Michael Nelson has joined Hartlepool as assistant manager while Lee Turnbull has been appointed in a consulting capacity to lead the club’s scouting and recruitment.
Chairman Raj Singh said: "It was always the view that we wanted to appoint a manager and coaching team that was modern in their approach, with the capability to build on foundations that have been put in place over recent years.
"Graeme joins us from Middlesbrough FC where has amassed a wealth of experience over a 10-year period and alongside Michael Nelson we believe we have two very forward-thinking coaches that are also strong and capable characters to lead the players and club forward.
"Graeme and Michael also know this level of football remarkably well having captained various sides in the Football League, they are natural leaders and both have a deep connection with our club having played nearly 500 games for Hartlepool United between them.
"I have great confidence that their commitment and work ethic will be second to none and I felt it was critical that we have people in the building who want to go the journey with us, to really unlock this club’s full potential.”