The Shakers had been without a boss since Richie Barker left to take charge of Crawley on the eve of the new season.
Peter Shirtliff had been in caretaker charge at Gigg Lane, but performances on the pitch ensured he would not be considered for the role on a permanent basis - with eight games played, they have just three points to their name.
Blackwell has previously managed Leeds, Luton and Sheffield United.