The announcement comes amid concerns Russian researchers might be cutting corners with the vaccine.
President Vladimir Putin said Tuesday that Russia had become the first country to approve a vaccine offering "sustainable immunity" against the coronavirus and that one of his daughters has been inoculated.
The announcement came after scientists in the West raised concerns about the speed of development of Russian vaccines, suggesting that researchers might be cutting corners after coming under pressure from authorities to deliver.
"This morning, for the first time in the world, a vaccine against the new coronavirus was registered" in Russia, Mr Putin said during a televised video conference call with government ministers.
"I know that it is quite effective, that it gives sustainable immunity," he said.
He said one of his daughters had been inoculated with the vaccine, developed by the Gamaleya research institute in coordination with the Russian defence ministry.
"In this sense she took part in the experiment," Mr Putin said, adding that she had a slight temperature after a second injection and "that's all".
"What counts most is for us to be able to ensure the unconditional safety of the use of this vaccine and its efficiency in the future. I hope that this will be accomplished,” he said.
Health Minister Mikhail Murashko said that clinical trials involving several thousand participants would continue.
The World Health Organization last week urged Russia to follow established guidelines and go "through all the stages" necessary to develop a safe vaccine.
The pandemic has seen an unprecedented mobilisation of funding and research to rush through a vaccine that can protect billions of people worldwide.
More than 100 possible vaccines are being developed around the world to try to stop the COVID-19 pandemic. At least four are in final Phase III human trials, according to WHO data.
Earlier, the Philippines said it was ready to work with Russia in testing and producing a vaccine.
"The Philippines stands ready to work with Russia on clinical trials, vaccine supply and production, and other areas deemed practicable by relevant Philippine and Russian agencies to address this global health emergency," a government statement said.
In a public address late on Monday, the country's outspoken president, Rodrigo Duterte, said: "When the vaccine arrives, I can be the first one to be experimented on ... If it is good for me, then it is good for everyone."
As of Monday, the Philippines's total number of confirmed coronavirus infections stood at 136,638, the highest in South-East Asia. The death toll from COVID-19 was 2,293.
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With additional reporting by Reuters.