Swiss, French and Russian experts were given samples to establish whether his death in Paris in 2004 at the age of 75 was the result of poisoning before the tomb was resealed.
France began a murder inquiry in August after Swiss experts found radioactive polonium-210 on his personal effects.
Arafat's medical records say he had a stroke resulting from a blood disorder.
His widow, Suha, objected to a post-mortem at the time of his death, but asked the Palestinian Authority to permit the exhumation "to reveal the truth".
Arafat's body lies in a stone-clad mausoleum inside the Muqataa presidential compound in the West Bank city of Ramallah. The mausoleum was sealed off earlier this month.
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Palestinian officials told Agence France Presse that only a Palestinian doctor had been allowed to directly touch the remains and remove the samples, but the process was conducted in front of the Swiss, Russian and French scientists, who will carry out tests for polonium-210 and possibly other lethal substances in their respective countries.
It is believed that the investigation could take several months.
Before the exhumation, the head of the Palestinian committee investigating Arafat's death, Tawfik al-Tirawi, said no journalists would be allowed to observe the exhumation.
"Because [of the] sanctity of the symbol and the sanctity of this event, [the exhumation] should not be permitted to be in front of the media," the former Palestinian intelligence chief said.
A reburial ceremony with full military honours had been planned, but this ultimately was not deemed necessary as the body was not removed from the grave during the collection of the samples.
Many Palestinians continue to believe Arafat was poisoned by Israel, which saw him as an obstacle to peace and had put him under house arrest.
There has also been speculation that Arafat was suffering from HIV or cancer at the time of his death.
Israel has strongly denied any involvement in Arafat's death.
An Israeli official, speaking on condition of anonymity, told the BBC: "All the medical files are in the hands of the family or the Palestinian Authority. For some reason they have not released them to this day. Our position has not changed over the years, but the question is why did they wait eight years?"