Tamošaitis was sentenced to 12 years imprisonment in a high-security penal facility.
Lithuania has insisted that his arrest and conviction is a retaliation for a Russian spy who was previously detained in Lithuania.
The Lithuanian's trial took place on March 17, but neither Russia's authorities nor the media had publicly announced it.
Tamošaitis could have filed an appeal against the sentence until Wednesday, but did not do so.
The Lithuanian was represented by a lawyer appointed by the Russian state. It was his decision not to file an appeal, as Vilnius can begin procedures to have him serve the sentence in Lithuania only after the verdict comes into effect, the country's Ministry of Foreign Affairs said.
“After the court verdict becomes official, the issue of handing over Tamošaitis to Lithuania could be handled on the basis of a bilateral agreement between Lithuania and Russia on transferring individuals sentenced to prison to serve their sentences in their home country, the Ministry of Foreign Affairs said to 15min.
Lithuania‘s Ministry of Justice is in charge of handling the handing over of prisoners, but it has yet to receive an official letter from Moscow informing about the conviction.
Tamošaitis was detained by the Russian Federal Security Service (FSB) officers for espionage on May 17, 2015, and accused of espionage. Russian media reported that the Lithuanian was arrested when he took secret documents from a recruited Russian citizen.
Moreover, Russian journalists said that the detainee confessed to working for the Lithuanian Army's Second Investigation Department, which carries out counter-intelligence.
Tamošaitis was arrested three weeks after a Russian citizen had been arrested in Lithuania for espionage. Intelligence officials said that the detainee was an FSB employee.