The Shakers, relegated to League Two last season, faced closure after revealing they needed to raise £1million to survive last month but have now been taken over by new chairman Stewart Day.
Blackwell was forced to release 16 players last week and only has eight contracted players on the books.
But he told the club website: "I can confirm I have met our new chairman and that I am absolutely delighted that Bury Football Club are at last giving me the support I have been asking for since I came to the club in September.
"I have been given full authority to bring in the right calibre of player and depth of squad in order to put this club back to where we should be.
"I am just so grateful the club's uncertain future has now been resolved, and I am looking forward to the new season with a more positive outlook."