The Shakers had been without a permanent manager since Richie Barker departed to take over at League One rivals Crawley in August, with Peter Shirtliff put in temporary charge.
Blackwell takes over at Gigg Lane having previously managed Leeds, Luton and Sheffield United.
During his time at Elland Road, the former goalkeeper guided Leeds to the Championship play-off final before losing to Watford, while he also went within one match of getting Sheffield United to the Premier League only to be denied again in the Championship's Wembley showpiece.
Bury are without a league win this season and lie bottom of the League One table with just three points from eight matches.
Blackwell's first game in charge will be at Stevenage on Saturday.