Flitcroft was only out of work for less than two weeks having been sacked by Barnsley on November 30 with the club sitting bottom of the Championship table.
Bury had initially agreed to stick with caretaker boss Ronnie Jepson until at least January, but chairman Stewart Day opted to move for Flitcroft when he became available, bringing the 39-year-old back to Gigg Lane where he spent two years as a player between 2004 and 2006.
"I have been a long-time admirer of David and what he achieved at Barnsley was a credit to him and to his philosophy of hard work and dedication. This is my first managerial appointment as a chairman and it needed to be the right one, hence I would not be rushed," PA quotes Day as saying.
"I am confident that after meeting with David and his team that we have secured the best manager available to take us to the next level and help us achieve the five-year goal. David is a dedicated individual that will not accept anything but the best for Bury Football Club.
"He had received offers from other clubs at a higher level, but he has bought into what we are trying to achieve at this club and has committed his future to take us back to where we belong, the Championship."
Flitcroft, whose contract length remains undisclosed, takes charge of a club two points off the relegation zone in League Two having won just four of their opening 19 games.