Flug, 62, is Israel's only female governor to date.
Prime Minister Benjamin Netanyahu and Finance Minister Moshe Kahlon officially announced the appointment on Tuesday afternoon.
Flug's successor still unknown, but decision was not impacted by uncertainty, she said.
Bank of Israel head Karmit Flug may be awarded a second term - once again by default.
Flug notified Prime Minister Benjamin Netanyahu of her decision on Thursday, according to a statement from the central bank.
A Finance Ministry spokesman said the hunt for a new Bank of Israel governor would begin after Passover.
Having a Swiss bank account is not illegal in Israel as long as it is reported to authorities and taxes are paid.
Proposal would spin credit card companies out from biggest banks, allow them to become banks in their own right.
The card features a centuries old trope of the hook-nosed Jew, wearing a kippah and a prayer shawl, rejoicing against the backdrop of gold coins.
New exhibit: Facing the British Lion — With Nothing but a Pencil