"The Israeli economy faces significant challenges," Flug said in a statement, adding that she looks forward to working with the bank and the government to "meet these challenges."
Her appointment still needs government approval, a step that is largely procedural and is expected to take a few days.
Fischer, who is widely credited with steering the Israel's economy safely through years of world financial turmoil, had recommended Flug for the post. But she was not Netanyahu's first choice.
Jacob Frenkel, a former central bank chief and Wall Street titan, withdrew in July after a committee questioned a shoplifting incident at a Hong Kong airport seven years ago. Frenkel said he mistakenly thought his companion paid for an item he was carrying.
In August, designated chief Leonardo Leiderman announced he was withdrawing. He did not give a reason, but the announcement came a day after an Israeli television channel reported that Leiderman regularly consulted with an astrologist.