In a gazette notification on Monday, the finance ministry's Bank and Financial Institutions Division said they would be in office for three years.
On Sunday, the government appointed Bangladesh Krishi Bank's Chairman Alauddin A Majid as the graft-hit bank's chairman.
Majid is a former managing director of the bank.
The move came after the specialised bank's chairman Sheikh Abdul Hye Bachchu tendered his resignation last Friday amid allegations of loan irregularities amounting to Tk 40 billion at three of its branches.
Managing Director Kazi Faqurul Islam was removed on May 25 after the allegations were raised.
Bangladesh Bank, finding the allegations to be true, recommended dissolution of the BASIC board on May 29.
The loan fraud, coming hot on the heels of the Hall-Mark scam involving another state-owned Sonali Bank, has become a source of embarrassment for the government.
Finance Minister Muhith said the board would be revamped and warned that none would be let off the hook if they were found involved in the irregularities.