In the 193-member General Assembly, 143 countries supported the resolution, while 35 nations – including China and India – abstained.
Four countries voted alongside Russia against the resolution – Belarus, Nicaragua, North Korea and Syria.
Moscow announced in September that it would annex four regions that were previously part of Ukraine.
“People have made their choice, and this choice is indisputable. Today we will sign agreements on the accession of the Donetsk People’s Republic, the Lugansk People’s Republic, the Zaporozhye Region and the Kherson Region,” Russian President Vladimir Putin said at a ceremony on March 30.
The UN resolution came a few days after Russia appealed a similar proposal in the Security Council, in which India had abstained from voting.
This week, tensions between Russia and Ukraine rose after the explosion of a bridge in Crimea, which led to missile strikes on major Ukrainian cities from Moscow.
UN chief Antonio Guterres condemned Russia’s action, saying he was deeply shocked and said it represented “another unsustainable escalation” in the war.