His family launched a case last month over claims that he was poisoned with polonium-210, a radioactive element.
Polonium was apparently found on some of Arafat’s belongings by Swiss scientists.
The medical records of Arafat, who died near Paris in 2004, say he had a stroke resulting from a blood disorder.
However, many Palestinians continue to believe Arafat was poisoned by Israel because he was an obstacle to peace. Israel has denied any involvement.
Others allege that he had Aids.
Yasser Arafat’s family lodged papers with the French authorities asking for an investigation in July.
The French news agency AFP on Tuesday reported that prosecutors had agreed to begin a murder inquiry.
The agency quoted unnamed sources close to the case.
Senior Palestinian official Saeb Erakat told AFP that the Palestinian Authority welcomed the inquiry.
He said Palestinian President Mahmoud Abbas had officially requested the help of French President Francois Hollande in the investigation.
“We hope there will be a serious investigation to reveal the whole truth, in addition to an international investigation to identify all the parties involved in Arafat’s martyrdom,” he said.
The inquiry stems from an Al-Jazeera TV documentary broadcast early in July.
The channel commissioned Lausanne University’s Institute of Radiation Physics to analyze Yasser Arafat’s belongings.
The scientists told the channel that they had found “significant” traces of polonium-210 present in items including Yasser Arafat’s trademark keffiyeh.
Following the documentary, Yasser Arafat’s widow Suha and daughter Zawra lodged a complaint with French judicial authorities.
Their lawyers have said they want a French investigation to work alongside international inquiries being conducted by the Lausanne scientists.
The French legal system is obliged to take the matter very seriously, given the diplomatic aspect of the affair, but the medical profession is generally skeptical about the claims of radioactive poisoning.
Last week, the Swiss institute said it had received permission from Suha Arafat and the Palestinian authorities to travel to Ramallah to analyze his remains.
Yasser Arafat led the Palestine Liberation Organisation for 35 years and became the first president of the Palestinian Authority in 1996.
He fell violently ill in October 2004 and died two weeks later, at the age of 75, in a French military hospital.
French doctors bound by privacy rules did not release information about Yasser Arafat’s condition.
In 2005, the New York Times obtained a copy of Yasser Arafat’s medical records, which it said showed he died of a massive haemorrhagic stroke that resulted from a bleeding disorder caused by an unknown infection.
Experts who reviewed the records told the paper that it was highly unlikely that he had died of AIDS or had been poisoned.
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