"Celtic Football Club can confirm that Martin O'Neill will be joining the club as manager until the end of this season," said a club statement.
"Martin will be supported by Shaun Maloney and Mark Fotheringham as assistants, as well as Stephen McManus, who will join our existing coaches, Gavin Strachan, Stevie Woods and Greg Wallace to oversee first-team matters."
The 73-year-old O'Neill stepped in as caretaker boss for eight games following Brendan Rodgers' exit in October, winning seven of those fixtures.
O'Neill, a full-time manager of the Glasgow giants from 2000 to 2005, stepped aside for Nancy in early December.
But the French boss was sacked on Monday after just eight games in charge, six of which ended in defeat.
O'Neill returns to take charge with Celtic still second in the table, six points behind leaders Hearts, following a 3-1 loss at home to arch-rivals Rangers.
Defeat in the Glasgow derby sparked protests outside Celtic Park by frustrated fans and proved the final straw for the club's hierarchy when it came to Nancy's continued employment.