At a brief ceremony in the Darbar Hall of Rashtrapati Bhawan, President Ramnath Kovind administered the oath of office to Misra.
Justice Misra took the oath in English in the name of God.
Justice Misra, 64, assumes office following the retirement of Justice J S Khehar yesterday.
Justice Misra will remain in office till October 2, 2018.
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He was the chief justice of the Patna High Court and the Delhi high court before being elevated to the apex court in October 2011.
After his enrolment as an advocate in 1977, Justice Misra practiced in constitutional, civil, criminal, revenue, service and sales tax matters in the Orissa High Court.
He was appointed as an additional judge of the Orissa High Court on January 17, 1996, before his transfer to the Madhya Pradesh High Court. He became a permanent judge on December 19, 1997.
He was also part of the bench that upheld the death sentence given to the convicts in the December 16, 2012 gangrape case.
Justice Misra, along with Justice P C Pant, had in May, declined to de-criminalise defamation - an offence punishable with two years in jail apart from fine - saying the right to free speech cannot mean that a citizen can defame anybody.
Former Prime Minister Manmohan Singh, Congress president Sonia Gandhi, leader of the opposition in the Rajya Sabha Ghulam Nabi Azad also attended the oath ceremony.