"At the end of the investigation... it has not been demonstrated that Yasser Arafat was murdered by polonium-210 poisoning," the three judges ruled, according to a statement from the prosecutor from the court in Nanterre near Paris told AFP.
Arafat died in Percy military hospital near Paris aged 75 in November 2004 after developing stomach pains while at his headquarters in the West Bank city of Ramallah.
His widow Suha has maintained he was poisoned, possibly by highly radioactive polonium.
But the judges ruled that there was "not sufficient evidence of an intervention by a third party who could have attempted to take his life," the prosecutor said.
Suha's lawyer, Francis Szpiner, also announced the judges' decision on Twitter.
Les juges de Nanterre viennent de rendre une ordonnance de non lieu dans l 'affaire de la mort de Yasser Arafat.
— Francis Szpiner (@fszpiner) September 2, 2015
La veuve de Yasser Arafat a décidé de faire appel de l'Ordonnance de non lieu
— Francis Szpiner (@fszpiner) September 2, 2015
She filed the murder case in 2012 at the Nanterre court. The same year, Arafat's tomb in Ramallah was opened for a few hours to allow three teams of French, Swiss and Russian investigators to collect around 60 samples.
Three French judges concluded their investigations in April and sent their findings to the Nanterre prosecutor, who recommended in July that the case be dropped.
A centre in the Swiss city of Lausanne had tested biological samples taken from Arafat's belongings that were given to his widow after his death, and found "abnormal levels of polonium."
It stopped short of saying that he had been poisoned by the substance.
French experts found that the isotopes polonium-210 and lead-210, found in Arafat's grave and in the samples, were of "an environmental nature," Nanterre prosecutor Catherine Denis said in April.
Lawyers for Arafat's widow accused the judges of closing the investigation too quickly and called for more experts to be questioned.
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