Buran, 62, a Massapequa resident and Independence Party member, replaces Thomas Stokes, who left the seven-member NIFA board in March to take a job as a consultant to Suffolk County Executive Steve Bellone.
Another board member, Robert Wild, disclosed Wednesday that he had resigned after relocating from Manhasset to New York City.
NIFA took control of Nassau's finances last year after finding a $176 million budget deficit.
Buran has been chief executive of the Lake Success-based Flushing Financial and its subsidiary, Flushing Savings Bank, since 2005, previously serving as its chief operating officer. He is a member of the Federal Reserve Bank of New York.
Campaign-finance records show Buran made a small contribution, $125, to Nassau County Executive Edward Mangano in March 2011. Federal elections records show Buran donated $2,300 to Republican Sen. John McCain's presidential campaign in 2008.
Mangano said in a statement, "I welcome new participation on the board."
Buran did not return calls for comment.
NIFA chairman Ronald Stack said, "We look forward to working with Mr. Buran."
With Celeste Hadrick