The two students, who had been camping at the JNU campus since Sunday night, surrendered at midnight. They drove from the administrative block to the main gate of the university and were escorted in a private security vehicle to an undisclosed location.
Mr Khalid and Mr Bhattacharya are likely to be produced before a magistrate today.
"Umar and Anirban have faith in the judiciary," JNU Students Union vice president Shehla Rashid told NDTV.
The police, however, told the court that they would not be able to manage law and order at a location chosen by the students.
The court said: "You can't use your whim and fancy. You have to follow the procedure, surrender or arrest. You have to be produced before a magistrate and he will decide whether you go into police custody or jail."
Umar Khalid and Anirban have been accused of organizing an event on February 9 to mark the anniversary of the hanging of terrorist Afzal Guru, in which anti-India slogans were raised.
Kanhaiya Kumar was arrested earlier this month for his alleged role in that event. He is in the Tihar Jail. His bail plea will also be heard by the high court today.
On Sunday night, Umar Khalid, Anirban and three other students accused of sedition, missing for days, showed up on the JNU campus and challenged the police to arrest them. The police were not allowed to enter the campus and said the students must surrender.