A screen at the UN in New York shows how some nations voted with green, red and yellow markers
The resolution was supported by 143 countries, while 35 states - including China and India - abstained.
As well as Russia, four countries rejected the vote, namely Belarus, North Korea, Syria and Nicaragua.
Although symbolic, it was the highest number of votes against Russia since the invasion.
Last week, in a grand ceremony in the Kremlin, President Vladimir Putin signed documents to make the eastern Ukrainian regions of Luhansk, Donetsk, Zaporizhzhia and Kherson part of Russia.
The agreements were signed with the Moscow-installed leaders of the four regions, and came after self-proclaimed referendums in the areas that were denounced as a "sham" by the West.
The resolution calls on the international community not to recognise any of Russia's annexation claim and demands its "immediate reversal". It welcomes and "expresses its strong support" for efforts to de-escalate the conflict through negotiation.
Ukraine's President Volodymyr Zelensky said he was grateful to the countries that supported it.
"The world had its say - [Russia's] attempts at annexation is worthless and will never be recognised by free nations," he tweeted, adding that Ukraine would "return all its lands".
US President Joe Biden said the vote sent a "clear message" to Moscow.
"The stakes of this conflict are clear to all, and the world has sent a clear message in response - Russia cannot erase a sovereign state from the map," he said.
Dame Barbara Woodward, Britain's ambassador to the UN, said Russia had failed on the battlefield and at the UN, adding that countries had united to defend the world body's charter.
"Russia has isolated itself, but Russia alone can stop the suffering. The time to end the war is now," she said.
The General Assembly vote was triggered after Russia used its veto power to prevent action at the Security Council - the body in charge of maintaining international peace and security. As permanent members, China, the United States, France and the United Kingdom also hold vetoes on the council.
There have been calls for Russia to be stripped of its veto power after the Ukraine invasion.
-- Courtesy of BBC News