The Chief Justice of Bangladesh's top court, Obaidul Hassan, agreed to resign "in principle" following intense pressure from protesters surrounding the Supreme Court, broadcaster Jamuna TV reported.
The 65-year-old judge will tender his resignation after consulting President Mohammed Shahabuddin in the evening, The Dhaka Tribune newspaper reported.
The protests started after Mr Hassan called for a full court meeting with all justices from both divisions of the Supreme Court. The protesting students viewed the convening of the full court meeting as a judiciary coup and announced a siege of the High Court premises.
In the face of student protest, Chief Justice Hassan postponed the meeting and later said that he would step down.
Hassan, appointed last year and seen as a loyalist to ousted Prime Minister Sheikh Hasina was given an one-hour ultimatum to resign.
Bangladesh Bank Governor Abdur Rouf Talukder has also resigned but his resignation has not been accepted given the importance of the position, finance ministry adviser Salehuddin Ahmed told reporters. Days earlier, four deputy governors were forced to resign by 300 to 400 bank officials accusing them of corruption.
The protests, part of the wider unrest that led to Hasina's departure, have resulted in over 450 deaths, including dozens of police officers. Hasina faces allegations of murder, forced disappearance, money laundering and corruption, and must face the law, Amir Khosru Mahmud Chowdhury, a senior member of Bangladesh Nationalist Party said.
The police union has declared a strike, refusing to return to work until their safety is assured, further complicating the situation.
Hasina has been sheltering in New Delhi since Monday and plans to return to the country and take part in elections.
Many homes and businesses of the country's minority Hindu community have also been vandalised this week, prompting hundreds of them in northwest Bangladesh to try and flee to neighbouring India.
Bangladesh's interim leader Muhammad Yunus appealed for religious unityas he embraced the weeping mother of a student shot dead by police, a flashpoint in mass protests that ended Sheikh Hasina's 15-year rule.
The Nobel laureate's first task is to bring stability to Bangladesh after he responded to a call by student protesters for him to temporarily lead the country following weeks of deadly anti-government demonstrations against the government led by Sheikh Hasina.