The Military Court of the Russian Pacific Fleet acquitted the two in connection with the incident in which 21 people, including 17 civilian shipyard workers, were suffocated to death on board the Akula II-class attack submarine.
Twenty one people were also injured in the incident.
The submarine was undergoing sea trials in the Sea of Japan when its freon gas-based fire suppression system was accidentally triggered.
The jury unanimously cleared them of the charges last Friday, Ria Novosti reported today.
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"I would like to thank all, who supported us these days. This verdict proves once again that people care about the fate of two Russian sailors," Lavrentyev said after the court's ruling.
Prosecutor Feliks Mamot said the prosecution will appeal the verdict in the course of the next ten days. The prosecution has the right to appeal the verdict before May 15.
The submarine was leased to the Indian Navy in 2011 and was formally commissioned into service as the INS Chakra II on April 4, 2012.