Lomaya has been in New York since the beginning of February, but until Tuesday's official ceremony did not have the right to vote in the UN as a permanent representative.
The new diplomat, who is close to Georgian President Mikheil Saakashvili, has replaced Irakli Alasania, who voluntarily left his position at the beginning of December and returned to Tbilisi to set up a coalition of Georgian opposition parties, the Alliance for Georgia. He is viewed as a frontrunner in the next presidential elections.
Lomaya has openly denounced Russia's intention to establish military bases in the former Georgian republics of Abkhazia and South Ossetia, which Georgia says remain integral parts of the country.
Russia recognized Abkhazia and South Ossetia as independent states two weeks after the end of a five-day war with Georgia last August. Fighting began when Georgian forces attacked South Ossetia in a bid to bring it back under central control.