Principal Magistrate Vishal Singh granted bail to the boy, who has just turned major, on furnishing a bond of Rs 50,000.
The board had earlier denied bail to the juvenile twice by observing that he was a repeat offender and had blamed his parents for allowing him to drive at such an age.
The boy sought bail saying he has given his 12th standard exams and has to appear in various entrance examinations and that he was depressed as he was away from his family.
He said the boy has already missed several exams during his stay in the reform home and he should be granted bail to enable him to appear in the rest of the examinations.
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The board had earlier asked the counsel to furnish the admit cards and other documents relating to the exams which were given to JJB.
The bail plea, however, was opposed by the police and prosecutor Atul Shrivastava sought to see the psychology reports of the boy.
The incident took place on April 4 when marketing executive Siddharth Sharma was trying to cross a road near Ludlow Castle School and the speeding Mercedes hit him.
The police booked the juvenile for the alleged offence of
culpable homicide not amounting to murder and he was sent to the reform home.
The police had said that the car was being driven at a speed of at least 80 km per hour and Sharma was flung several feet in the air by the impact of the crash.
The police had earlier arrested a man who claimed to be the actual driver of the Mercedes at the time of incident but did a volte-face after he got to know the victim was dead.
The driver and the boy's father, who was also arrested earlier, were granted bail by the court.
The youth had appeared before a Delhi court to surrender and moved a bail plea which was rejected on the ground that it was a matter of JJB. He was then produced before the board.