The 34-year-old joined the Dark Blues as a player in 2014 before moving into a coaching role at the Kilmac Stadium at Dens Park.
The former Livingston, Coventry City and Hibernian defender will be assisted by Jimmy Nicholl, who leaves his post as No 2 at St Mirren.
McPake and Nicholl have signed rolling contracts with Dundee, who are looking to make an immediate return to the Ladbrokes Premiership following relegation in 2018/19.
