"We were impressed by Dr. Flug's performance as head of the Bank of Israel over the past months, and are certain she will help us march Israel's economy to further achievements in face of the global economic upheaval," Prime Minister Benjamin Netanyahu and Finance Minister Yair Lapid said in a statement.
Flug, 58, served as deputy governor of the bank since 2011 and took the helm temporarily after Stanley Fischer stood down on June 30 after a successful eight-year run.
Her appointment comes after Netanyahu and Lapid tapped two well-known economists, Jacob Frenkel and Leo Leiderman, both of whom withdrew their candidacy following reports of impropriety.
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Flug was chosen over three other final candidates: Tzvi Eckstein and Victor Medina, both former deputy governors of the bank, and former Argentine central bank governor Mario Blejer.
Justice Minister Tzipi Livni hailed the nomination, which she said showed that people didn't "fear to appoint a woman to a senior financial position, despite it being considered 'masculine'."
Livni wrote on her Facebook page she was sure Flug would succeed in the position "not because she is a woman, (but) because she is a worthy professional."
Flug thanked Netanyahu and Lapid and said she looked forward to working with the bank's staff and with government officials to meet the challenges facing the Bank of Israel and the Israeli economy, a bank statement said.