0615 GMT July 21, 2019
The departure of the Houthis on a Kuwaiti plane followed a prisoner swap deal and the evacuation of 50 wounded fighters for treatment in Oman in a major boost to peace efforts, AFP wrote.
The delegation was accompanied by UN envoy Martin Griffiths, an airport source said.
Houthi spokesman Mohammed Abdelsalam confirmed their departure on Twitter, saying the Houthis "will spare no effort to make a success of the talks to restore peace and end the aggression".
At the same time he called on Houthi fighters to remain "vigilant against any attempt at a military escalation on the ground".
Although no date has been announced for the start of the talks, Yemeni sources say they could get under way on Thursday.
The agreement to exchange hundreds of detainees was welcomed by the International Committee of the Red Cross, which will oversee the swap after the first round of planned peace talks in Sweden.
The deal was struck by Griffiths, who was in the Houthi-held capital Sana’a for meetings already buoyed by the evacuation of the wounded fighters – a key Houthi precondition for the talks.
A previous UN-brokered attempt to bring the Houthis and the Saudi-backed forces to the negotiating table collapsed in Switzerland in September.
The United Arab Emirates, another key backer of Yemen’s former government, said the planned talks offered a "critical opportunity" to end nearly four years of war.
Hadi Haig, an official of the former government, said between 1,500 and 2,000 members of Saudi-backed forces and between 1,000 and 1,500 Houthis fighters would be released.
On the former government side, they include ex-defense minister Mahmoud al-Subaihi, who has been held by the Houthis ever since they overran the capital in late 2014, and former president Abed Rabbuh Mansur Hadi's brother Nasser, a general and former senior intelligence official.
Houthi official Abdel Kader al-Murtadha confirmed the deal, adding that he hoped it would be "implemented without problem".
ICRC spokeswoman Mirella Hodeib welcomed the agreement, saying: "This is one step in the right direction towards the building of mutual trust among Yemeni communities."
Thousands of prisoners have been captured by both sides in the grinding war of attrition that has devastated Yemen.
The resulting humanitarian crisis, already the world's worst, will deteriorate in 2019, the UN said Tuesday, warning that the number of people needing food aid is set to jump by four million.
Overall, 24 million people in Yemen – roughly 75 percent of the population – will need humanitarian assistance in 2019, UN humanitarian chief Mark Lowcock told reporters in Geneva.
He said the dire figures underlined the importance of the planned peace talks in Sweden.
If the negotiations show results, "it is possible that we could find by the second half of the year that the extreme edge could get taken off the suffering of those people who have no form of income," he said.
Kuwait's Deputy Foreign Minister Khaled al-Jarallah earlier told reporters that his country's ambassador to Yemen would also accompany the Houthi delegation travelling to Stockholm.
The oil-rich Persian Gulf emirate has been a mediator in the devastating conflict.
International support for the new peace bid has been spurred by UN warnings that 15 million Yemenis are at risk of famine as the humanitarian situation deteriorates.