After repeatedly delaying their departure, the delegation left from the capital Sanaa aboard a UN plane for the Swiss city, where the talks are due to start tomorrow, a day late.
The UN's peace envoy for Yemen, Ismail Ould Cheikh Ahmed, said in a statement that Monday would see the start of "preliminary inclusive consultations" bringing together the country's warring factions for the first time.
He appealed for participants to take part "in good faith and without pre-conditions, and in a climate of trust and mutual respect".
The rebels, supported by military units loyal to ex-president Ali Abdullah Saleh, have seized control of large parts of the country including Sanaa, forcing Hadi to flee to Saudi Arabia.
Fearing an Iran-friendly regime on its southern border, Riyadh has been leading a campaign of air strikes against the rebels since March 26 but has so far failed to force them from territory they have seized.
Today the rebels faced little resistance as they took control of Al-Hazm, the main city of Jawf province, residents and pro-government fighters said.
Analysts say the conflict has reached a deadlock and pressure has been mounting for an attempt at a political solution.
The rebel delegation that left Sanaa today included five representatives from the Huthis and Saleh's General People's Congress party, an aviation official and a source close to rebels told AFP.
Hassan Zaid, the head of Shiite opposition party Al-Haq, was also in the delegation and two other Huthis were heading to Geneva from neighbouring Oman.
Representatives of Hadi's government had arrived yesterday for the talks, which had been due to start today but were delayed after the rebels refused to board a UN plane that had been scheduled for a stopover in Saudi Arabia.
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