The defendants, charged with "terrorist activity" and with "violently seizing or retaining power," were sentenced to between 13 and 23 years in prison, Russian state media reported.
Independent news outlet Mediazona said 11 other people whom Russia had already returned to Ukraine in prisoner exchanges were also sentenced in absentia.
They included nine women who had worked as army cooks.
It said the 12 Azov members, who appeared in court with shaven heads, would appeal the verdicts and that some of them had denied wrongdoing or had said that testimony they had given had been obtained under duress, something Reuters was not able to confirm.
There was no immediate Ukrainian comment on the verdicts.
The Azov regiment, which is banned inside Russia, has been a special focus of Russian anger, often characterised as a fanatical grouping of Russia-hating neo-Nazis.
Ukraine rejects Russia's description of Azov as a terrorist organisation.
The regiment was founded by hardline ultranationalist Andriy Biletskiy but subsequently dissociated itself from his politics.
From 2014, the militia was folded into the National Guard and Ukraine says it was reformed away from its radical nationalist origins and is now apolitical.
For many Ukrainians, Azov fighters are heroes who came to symbolise the spirit of national resistance, clinging on in the devastated ruins of Mariupol as Russia besieged the port city between February and May 2022.
Russia said nearly 2500 eventually surrendered, emerging from their refuge in a vast network of bunkers tunnels beneath the city's Azovstal steelworks.
The Kremlin said at the time that President Vladimir Putin had guaranteed that they would be treated according to international standards.
Prior to Wednesday's sentences, the head of Russia's state Investigative Committee said earlier this month that Russian courts had so far convicted 145 Azov members.
