Stepic, 66, credited with helping Raiffeisen become a major lender in central and eastern Europe, said that his decision to end his 40-year career at the bank was "to avoid any damage to Raiffeisen's reputation".
Not taking questions from reporters, Stepic said that the investments reported by the News weekly were made in good faith on advice from Swiss bank UBS and were not "offshore" vehicles aimed at evading tax.
According to News, they involved two firms based in the British Virgin Islands and in Hong Kong that Stepic, a widely respected figure in the banking sector, used to buy two apartments in Singapore in 2006 and 2008.
His resignation comes amid international efforts to crack down on tax evasion, with European Union leaders this week targeting a year-end deadline to undo banking secrecy.