He replaced T Vaiphei who served in the post since 2016.
Governor Tathagata Roy administered him the oath of office and secrecy at Rajbhavan here.
"It's a privilege to be a chief justice here. I will try my best to deliver services to this institution. I shall do whatever is possible for me," Rastogi told reporters.
Supreme Court Chief Justice Dipak Misra, Justice J Chelameswar and Justice Ranjan Gogoi had earlier signed the SC collegium's recommendation on Rastogi's appointment.
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