Justice Surendra Kumar Sinha was the first top judge in Bangladesh to have stepped down.
The president's office said on Saturday that they received a letter of resignation from Sinha, who is now abroad.
Sinha was appointed to the top court as the chief justice in January 2015, with his term scheduled to end on Jan 31, 2018.
He came under fire from the ruling party after the Supreme Court scrapped a constitutional amendment to sack higher court judges.
Bangladesh parliament passed the constitution's 16th amendment in 2014, which empowered lawmakers to investigate and sack top judges on the grounds of incapability and misconduct.
The verdict revived the Supreme Judicial Council, a provision brought during military ruler and BNP founder Ziaur Rahman's regime, to remove top court judges.
The Supreme Court published the full verdict on Aug 1, drawing harsh criticism from the Awami League government.
The Awami League accused him of 'belittling' the Father of the Nation Bangabandhu Sheikh Mujibur Rahman in some of the observations.
Chief Justice Sinha sat in his office for the last time on Aug 24 before the annual vacation of the apex court started.
The government announced his 'sick' leave on Oct 3, a day before the vacation ended.
Justice Md Abdul Wahhab Miah became acting chief justice then and the government said in a circular that he would act as chief justice until the end of Justice Sinha's leave or his return.
Justice Sinha left Bangladesh for Australia on Oct 13. Before leaving, he issued a statement, saying he was 'not sick' and the criticism over the verdict 'embarrassed' him.
A day after his departure, the Supreme Court in a rare statement described Justice Sinha's statement as 'misleading'.
According to the Supreme Court statement, Justice Sinha faces 11 specific charges, including graft, money laundering and moral lapse, for which his colleagues in the Appellate Division refused to work with him.
According to the Bangladesh Constitution, if the chief justice's office becomes vacant, the next most senior judge of the Appellate Division will perform his duties.
On Oct 3, the day the government announced Justice Sinha's 'sick leave', a government order said the president appointed Justice Abdul Wahhab Miah as the acting chief justice.
Later on Oct 12, a day before Sinha left the country, a second order was issued which said Justice Miah will head the Supreme Court until the end of Sinha's leave or his return.
With Justice Sinha stepping down from his office, Justice Miah will perform the duties of the chief justice until a new appointment.