The Saudi-led alliance intervened in the civil war in 2015 after the Houthi movement ousted Hadi's government from the Yemeni capital Sanaa in 2014.
The talks mark the first meeting between Yemen's legitimate government and Houthi militants, backed by Iran, since 2016, when 106 days of negotiations yielded no breakthrough in a war that has pushed 14 million people to the brink of starvation.
One representative of the internationally recognised government, Abdullah al-Alimi, tweeted that the talks were "a true opportunity for peace", before the delegation flew out of the Saudi capital Riyadh on Wednesday.
The Huthi rebels arrived on a Kuwaiti plane from Sanaa following a prisoner swap deal and the evacuation of 50 wounded insurgents for treatment in Oman in a major boost to peace efforts.
The Houthis have said they would head to Sweden once the wounded were evacuated and if their delegation's plane was not inspected by the coalition.
Peace talks between the Yemeni government and rebels, aimed at ending four years of war that has pushed 14 million people to the brink of starvation, were due to open Thursday in Sweden.
The United Arab Emirates (UAE), another key backer of the government, said the planned talks offered a "critical opportunity" to end almost four years of war.
The departure of the 12-member delegation headed by Foreign Minister Khaled al-Yamani followed the arrival in Sweden of the rebel negotiating team.
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The UN food agency said it was planning to scale up food distribution rapidly to help another four million people in Yemen over the next two months, more than a 50 per cent rise on the number now reached.
"We expect both parties to be realistic and flexible and hopefully we will succeed in confidence-building measures and make progress", he said in Arabic, in a video posted on social media Tuesday.
The oil-rich Gulf emirate, which has been a mediator in the devastating conflict, hosted Swedish Foreign Minister Margot Wallstrom for talks in Kuwait City on Monday.
Outrage over the October 2 murder of Saudi journalist Jamal Khashoggi in the Saudi consulate in Istanbul has intensified global scrutiny of Saudi activities in the region, potentially giving Western powers, which provide arms and intelligence to the coalition, more leverage to demand action.
The coalition has largely suspended its offensive on Hodeida in the face of US-led calls for a ceasefire and new peace talks.
"UN Security Council Resolution 2216 offers a workable road map".
"A stable state, important for the region, can not coexist with unlawful militias", he said.
But the Houthis are unlikely to agree to withdraw from territory or to lay down their arms, as the Yemeni government has demanded repeatedly.
Any power-sharing agreement, or even tentative transitional government, would have to contend with Yemen's convoluted political and military constitution.