Their investigation was one of three carried out on his remains and items he had when he died in Paris in 2004.
Last month, Swiss scientists said they had detected high levels of radioactive polonium but could not say if it had caused his death.
A French inquiry is also said to have found he was not a victim of poisoning.
Yasser Arafat fell ill after eating a meal in his compound in Ramallah and weeks later was admitted to hospital in France, where he died.
He was diagnosed with a serious blood disorder and died of a stroke on 8 November 2004. But no post mortem examination was carried out as his widow Suha did not ask for one.
When in 2012 an investigation by al-Jazeera TV in conjunction with Swiss analysts in Lausanne found abnormal levels of polonium-210 on his personal effects, Suha Arafat called for her late husband’s body to be exhumed.
France then launched a formal murder inquiry.
The Vaudois University Hospital Centre (CHUV) in Lausanne reported its findings last month, on the ninth anniversary of his death, saying its results “offer moderate backing for the theory of poisoning”.
But a leaked report of Russia’s initial tests on the same day said high radioactive penetration was “unsubstantiated”. Weeks later, a source said the French report had ruled out the poisoning theory, and pointed towards a natural death.
Announcing its conclusions on Thursday, the head of Russia’s Federal Medical-Biological Agency (FMBA), Vladimir Uiba, said “Yasser Arafat died not from the effects of radiation but of natural causes”.
The agency had completed its work, he said, and there was general agreement with its findings. “Even the Swiss withdrew their statements and agreed with us, and the French confirmed our conclusions,” Mr Uiba was quoted as saying by Interfax.
Palestinian ambassador to Moscow Faed Mustafa said investigations into the former Palestinian Authority president’s death would go on.
“We respect their position and we highly value their work, but there is a decision to continue work,” he said according to Russia’s Ria Novosti.
Many senior Palestinian officials have blamed Israel for the death, although Israel has strenuously denied having anything to do with it.
Yasser Arafat’s widow told the BBC last month that her husband had “a lot of enemies” but she could not accuse anybody or jump to conclusions.
The Swiss expert who examined samples of Yasser Arafat’s remains dismissed as a “political declaration” a statement Thursday by Russian researchers excluding radiation poisoning as the cause for the Palestinian leader’s death.
“The Russians, they make claims without providing any data, without providing any scientific arguments, for me that is empty, a political declaration,” said Francois Bochud, director of the Lausanne Radiophysics Institute.
Bochud criticised the Russians for not releasing their report.
Bochud was the co-author of a report released on November 7 that found high levels of polonium, up to 20 times the normal level. It said the findings were consistent with radioactive poisoning without saying conclusively that Arafat’s death was due to the polonium.
Some 60 samples were taken and divided between Swiss and Russian investigators as well as a French team carrying out a probe at the request of Arafat’s widow, Suha.
Bochum said that the Swiss had not received a copy of the Russian study, and that Palestinian officials who had seen it said the results were similar to the Swiss data.
“But to claim the opposite with same data seems to be really fallacious,” said Bochud.
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