Darcy Christen, a spokesman for the lab at the Lausanne University Hospital Centre, told AFP they were waiting for a formal lawyer's letter before travelling to Ramallah to carry out the probe.
"Time is of the essence, you could say it's a question of weeks, not months, because the traceability of polonium diminishes by half every 138 days," Christen said, noting that this has occurred 20 times since Arafat died aged 75 on November 11, 2004.
The Palestinian Authority also approved the probe, which was requested by Palestinian president Mahmud Abbas after a media investigation found elevated levels of polonium on some of Arafat's belongings, including clothing he wore before he died at a military hospital outside Paris.
A statement from French lawyers acting for Arafat's widow Suha Arafat and their daughter Zawra welcomed the authority's comments.
"We are glad that the position of the Palestinian Authority is to accept the exhumation of the body of Yasser Arafat," Pierre-Olivier Sur and Jessica Finelle wrote.
"However, we consider that this act of enquiry should be in coordination with the French investigating system... which should appoint an investigating judge to conduct the necessary enquiries," the statement said.
It added that such an appointment must be made "very quickly: it is a matter of weeks or even days from now."
In the West Bank city of Ramallah, where Arafat is buried, Tawfiq Tirawi, head of the Palestinian committee probing his death, told AFP on Friday that he had "not so far been officially informed" of a decision by the Swiss lab.
French doctors had offered no explanation for Arafat's death, and many Palestinians believe he was poisoned by Israel, which denies the allegations.
Suha and Zawra Arafat lodged a complaint for murder against persons unknown in France on July 31 over the radioactive poisoning claims.
Their lawyer in Geneva, Marc Bonnant, told Swiss television on Thursday that she "wanted this investigation... she's the one pushing for it, and as a result we will go to Ramallah," the de facto capital of the occupied West Bank.
Polonium is a highly toxic radioactive substance that is rarely found outside military and scientific circles. It was used to kill Russian former spy turned Kremlin critic Alexander Litvinenko, who died in 2006 after drinking tea laced with the substance in London.
The Swiss team will first carry out a fact-finding mission during which they will meet representatives of the Palestinian Authority, inspect Arafat's mausoleum and assess technological and scientific capabilities on the ground, Christen said.
If they deem the testing to be viable, they will carry out a second mission to take samples from the body.
The Swiss experts were among several specialists consulted by the Al-Jazeera news channel, which commissioned the analysis of Arafat's personal effects.
By Pierre Taillefer