Riyadh announced $US3 billion in financial aid to the Saudi-backed government after the announcement by President Abd-Rabbu Mansour Hadi.
It called for talks with the Houthi group that controls the north and has been battling a Saudi-led coalition.
Yemen's warring sides had in a major breakthrough agreed a two-month truce that began on Saturday, the first since 2016.
The truce also eased a coalition blockade on areas held by the Houthis, who ousted Hadi's government from the capital Sanaa in late 2014.
"I irreversibly delegate to the Presidential Leadership Council my full powers in accordance with the constitution and the Gulf Initiative and its executive mechanism," Hadi, who is based in Riyadh, said on state television.
Dismissed Vice President Ali Mohsen al-Ahmar, an Islamist-leaning general, is resented by the Houthis for military campaigns in their northern stronghold and by some southerners for his role in the 1994 north-south civil war.
Hadi took the helm of a crumbling state a decade ago in a Gulf-backed transition plan after protests that brought down President Ali Abdullah Saleh, who was later killed.
Riyadh, which has struggled to exit the war in Yemen, urged the new council to negotiate with the Iran-aligned Houthis under UN auspices "for a final and comprehensive solution".
"This is an attempt, perhaps a last ditch effort, to reconstitute something resembling unity within the anti-Houthi alliance. The problem is that it is unclear how these various individuals, many of whom have diametrically opposing views, can work together," Gregory Johnsen, a former member of the United Nations' Panel of Experts on Yemen, said on Twitter.
Saudi de facto ruler Crown Prince Mohammed bin Salman was shown in a video on state media meeting with the new eight-member council, which is led by Rashad Al-Alimi.
Alimi is close to major bloc the Islamist Islah party, a backbone of Hadi's government which is distrusted by coalition partner the United Arab Emirates.
The council includes leaders of UAE-backed factions, including Aidarous al-Zubaidi of the separatist Southern Transitional Council, which vied with Hadi's government for control of Aden.
The war has killed tens of thousands, devastated the economy and pushed Yemen to the brink of famine. The central bank split into rival authorities and the riyal's depreciation in the government-held south pushed basic goods out of reach for many.
Saudi Arabia and the UAE will each inject $US1 billion into Yemen's central bank and the kingdom will grant an additional $US1 billion for oil derivatives and development, said a statement on Saudi state media.
Riyadh, which last deposited funds into the Aden-based central bank in 2018, also said it would give $US300 million to the UN aid response, which in March raised less than a third of the $US4.27 billion sought.
The United Nations is pushing for measures to stabilise the economy and launch inclusive political negotiations to end the conflict in which several Yemeni factions are vying for power.
The war is widely seen in the region as a proxy war between Saudi Arabia and Iran. The Houthis say they are fighting a corrupt system and foreign aggression.
