District and Sessions judge Gautam Debnath ordered Sinha be sent to Kailashahar Sub-Jail under tight security.
Sinha had been sentenced on November 11, 2013 by the District and Sessions court to three-month imprisonment on the charge of violating the Arms Act in connection with the Babur Bazar firing incident on July 20, 2004 which caused the death of two persons - CPI(M) leader Abdul Hannan and Nikhil Deb, personnel guard (PG) of the Congress MLA.
The veteran leader then challenged the verdict and sought leniency from the Tripura High Court which on hearing the case on September 7 last upheld the district court's judgment.
Today's surrender is in accordance with the Supreme Court's directive on the issue.
The apex court is slated to take up the petition again on November 2.
Sinha is a sitting Congress legislator since 1988 and a former member of the All India Congress Committee.