No one knows for sure.
His remains were exhumed in November 2012, and samples were taken by Swiss, French, and Russian research teams.
The Swiss report was made public in November of 2013. It's available here if anyone wants to crawl through all 108 pages of it. According to the news media, they said that
taking into account analytical limitations such as the time elapsed since Mr. Arafat’s death, its findings "moderately support the proposition" that the death was the consequence of polonium poisoning.
CNN goes into a bit more detail on those "analytical limitations":
Eight years passed between the death and the exhumation. Because polonium-210 has a half-life of just 138 days, its detection after eight years is "very difficult and subject to uncertainties."
Effectively, their conclusion was that his body made the surroundings more radioactive. They deliberately didn't definitively conclude whether that was because he was deliberately or accidentally poisoned, or whether there was some other cause - just that it supported the theory.
The french report was never released to the public, but had portions leaked anonymously and was spoken about by Arafat's widow. Reportedly (BBC, CNN, NY Times), the team found higher-than-normal traces of polonium, but concluded he died from a "generalized infection". They concluded that the polonium came from the environment and made his remains radioactive after his death.
The Russian report has also not been released to the public, and has been discussed even less than than the French. There was an early leak (later denied) that they hadn't found any polonium at all, but they have officially said that he died of natural causes (not polonium poisoning) (BBC NY Times).
Just to confuse things more, the BBC article has this interesting quote:
The agency had completed its work, [the head of Russia's Federal Medical-Biological Agency, Vladimir Uiba] 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.
However, Francois Bochud, the head of the Lausanne institute that carried out the parallel Swiss inquiry, told AFP news agency the Russian findings had no scientific foundation.
Where does this leave us?
As stated above, no one knows for sure. As far as I can tell, both the French and Palestinian investigations (who both have access to the full reports) are still open, which implies that there was nothing obviously wrong with any of the reports. No one has come forward with an explanation of why they disagree.
His symptoms (according to Wikipedia) are consistent with the effects that polonium can cause, including liver and kidney damage, nausea, vomiting, and so on. However, there are many conditions and diseases that would also cause those symptoms, so there's nothing conclusive there.
It's absolutely possible that Arafat died due to polonium poisoning, but it's been way too long since 2004 to be able to prove it one way or the other. The scientists can't agree, and no one else has more than theories.