"I believe that in order to facilitate the work of [investigators], the right thing would be to place my resignation at the disposal of the president of the republic, which I did," said Michael Sarris, who was finance minister for just five weeks.
He was named chairman of the bank, also known as Laiki Bank, in January 2012 as part of a drive to strengthen the giant troubled lender's capital position. He stepped down in August.
The bank's failure helped propel the country to the brink of financial meltdown.
The bank was shut down as part of the bailout deal announced last week.
During a previous finance minister term between 2005 and 2008, Sarris -- a former senior World Bank official who earned a doctorate in economics at Detroit's Wayne State University -- orchestrated Cyprus' entry into the eurozone.
Cypriot President Nicos Anastasiades accepted Sarris' resignation and appointed Labor Minister Harris Georgiades in his place.
Anastasiades said Sarris' decision to step down "for reasons of political responsibility, in order to ease the work of the investigating committee, constitutes an example of a new mindset in Cypriot political life."
The announcement came hours after Anastasiades swore in three top judges charged with investigating how the country was led to near-bankruptcy.
The judges have sweeping powers to probe allegations top officials and their family members -- including at least one Anastasiades relative -- used advance knowledge of the country's bailout deal to protect their assets.
The deal required deposits of 100,000 euros or more to be hit with heavy losses.
Among the well-connected Cypriots, Russians and Ukrainians who allegedly made last-minute transfers to avoid the financial hit on their uninsured deposits was the president's son-in-law, Yannos Loutsios.
Cyprus' Sigma TV and Communist Party newspaper Haravghi reported A. Loutsios & Sons Ltd., said to be co-owned by Loutsios, husband of Anastasiades' daughter Elsa, allegedly made use of insider information to transfer more than $25 billion out of Laiki Bank days before its collapse.
The Loutsios family and Anastasiades have denied any wrongdoing.
The judges are to deliver a report to the attorney general by July, opening the way for possible prosecutions of prominent Cypriot bankers, lawyers and accountants, the Financial Times reported.
Cyprus is to receive the first part of its bailout cash next month and has promised to start repaying its loans at a rate of 2.5 percent in 10 years, officials said Tuesday.
The Cypriot government agreed to meet bailout conditions, including getting its budget to a 4 percent surplus, by 2018, a two-year extension from the original target imposed by the so-called troika of official lenders -- the eurozone, the International Monetary Fund and the European Central Bank.