Atiur Rahman, 64, resigned over after a meeting with Prime Minister Sheikh Hasina.
"He (Rahman) has tendered his resignation to the Prime Minister," a Premier's office spokesman told PTI.
Prime Minister's press secretary Ihsanul Karim said Rahman met Hasina at her office in the morning and handed over his resignation, seven years after he was appointed as the Governor of Bangladesh Bank.
During his tenure, Rahman, a development economist, launched a series of populist policies to take bank services to the doorstep of millions of rural people in Bangladesh.
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His resignation came weeks after the central bank confirmed that the huge amount was stolen from its account in Federal Reserve Bank of New York, sparking a worldwide uproar.
Bank spokesman had said that unknown hackers had stolen USD 101 million of which USD 81 million entered the Philippines and the rest went to Sri Lanka to be used in casino business.
Finance Minister AMA Muhith had earlier said he was kept in the dark about the heist for weeks, adding that the central bank management must explain its "audacity".
He said that the government today decided to appoint former finance secretary and incumbent chairman of state-run Sonali Bank, Fazle Kabir, as the new Governor of Bangladesh Bank (BB).
"Fazle Kabir is now in New York...He will join as the central bank governor office next week," the minister said.
The heist took place on the night of February 4, using information stolen through the malware, which sent a total of 35 transfer orders to the New York Federal Reserve Bank where the Bangladesh's central bank has an account.
into the heist and campaign to return the stolen money.
The government today formed a three-member "high-powered" committee with former central bank governor Farash Uddin as its chairman to investigate the matter and identify the people responsible for the security breach.
The Bangladesh Bank officials said the hackers tried to stole a further USD 850 million, but the bank's security systems and typing errors in some requests thwarted the full theft.
The US Reserve Bank, which manages the Bangladesh Bank reserve account, denied its own systems were breached.
Filipino authorities have recovered some of the stolen money and launched an extensive investigation into the fraud by hackers suspected to be Chinese Pilipino.