The appointment, which follows open competition, will take place immediately.
Mr Bull, who succeeds Ian Stewart, has been the acting Director in BFI since May this year.
Bull worked at the National Audit Office from 1979-1996, and has been a consultant to the Swedish International Development Authority. He was educated at the University College of Wales, Aberystwyth.
The BFI is an independent unit within the Department of Social Security set up to inspect social security benefits administration and counter-fraud activity within DSS agencies and local authorities, and to promote good practice.
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