Griffiths, the United Nations envoy, hopes to reach a deal on reopening Sanaa airport, implementing the prisoner swap and agreeing to a detente in the critical Yemeni port city of Hodeidah, which could serve as a foundation for a wider ceasefire.
A UN-chartered flight left Sanaa with 50 wounded rebels on board and landed in Muscat, Oman's official ONA news agency reported.
The coalition said in a statement it had agreed on the evacuation for "for humanitarian considerations and as part of confidence-building measures" ahead of the talks, which are also due to focus on a transitional governing body.
A Houthi rebel delegation prepares to fly on a Kuwaiti plane accompanied by the UN's peace envoy from Sanaa on Wednesday.
The evacuation marked a key step in kickstarting stalled negotiations as world powers press for an end to the devastating conflict that has pushed Yemen to the brink of starvation.
The 13-member team, headed by Yemen's Foreign Minister Khaled Yamani, departed Saudi Arabia to engage in direct negotiations with the delegates of Houthi rebels in Sweden's capital Stockholm, a government source said on condition of anonymity.
However, Yemeni Minister of Information Daifallah al-Shami said that the Houthis had not received any official invitation for the UN-mediated peace talks in Sweden.
Wounded rebels were transported across the capital, controlled by the insurgents since 2014, in ambulances as they made their way to the long-defunct airport.
Although no date has been announced for the start of the talks, Yemeni government sources say they could get under way on Thursday.
Griffiths hopes to reach a deal on reopening Sanaa airport and securing a prisoner swap and a ceasefire in Hodeidah as a foundation for a wider truce, including a halt to coalition air strikes that have killed thousands of civilians and Houthi missile attacks on Saudi cities.
The opposing sides have cautiously reiterated their willingness to attend negotiations.
A previous attempt by Griffiths to hold UN-sponsored talks in Geneva collapsed in September when the rebels failed to appear.
The first Yemen talks since 2016 are widely seen as the best chance yet for peace, as the global community throws its weight behind resolving the devastating conflict that has pushed the Arab world's poorest country to the brink of starvation.
A delegation from Yemen's internationally recognised government is expected to arrive in Sweden on Wednesday, a Yemeni official told The National.
The United Nations says the humanitarian crisis in Yemen, already the worst in the world, will deteriorate in 2019, almost four years after a military coalition led by Saudi Arabia invaded the impoverished country and began an intense campaign of airstrikes and ground attacks which are still ongoing.
The coalition spokesman said military operations in Hodeida were "ongoing" on Monday.
Human rights groups put the death toll far higher.