The body replaces the military council that took charge after the ouster of Omar al-Bashir.
General Abdel Fattah al-Burhan will be Sudan's head of state for the first 21 months of the 39-month transition period, until a civilian takes over for the remainder.
It is the first time that Sudan is not under full military rule since Bashir's coup d'etat in 1989.
Sudan took further steps in its transition towards civilian rule Wednesday with the swearing in of a new sovereign council, to be followed by the appointment of a prime minister.
The body replaces the Transitional Military Council (TMC) that took charge after months of deadly street protests brought down longtime ruler Omar al-Bashir in April.
As a result of Wednesday's move, it was the first time that Sudan was not under full military rule since Bashir's coup d'etat in 1989.
The first steps of the transition after the mass celebrations that marked the August 17 adoption of a transitional constitution proved difficult however.
Sovereign council
The names of the joint civilian-military sovereign council's 11 members were eventually announced late Tuesday after differences within the opposition camp held up the process for two days.
General Abdel Fattah al-Burhan, who already headed the TMC, was sworn in as the chairman of the new sovereign council in the morning.
Wearing his usual green beret and camouflage uniform, Burhan took the oath in a short ceremony, one hand on the Koran and the other holding a military baton under his arm.
He will be Sudan's head of state for the first 21 months of the 39-month transition period, until a civilian takes over for the remainder.
The council's 10 other members were sworn shortly afterwards and Abdalla Hamdok, who was chosen by the opposition last week to be prime minister, was to be formally appointed later Wednesday.
The sovereign council includes two women, including a member of Sudan's Christian minority, and it will oversee the formation of a government and of a legislative body.
The inauguration of a civilian-dominated ruling council was welcomed by Khartoum residents but many warned the people would keep their new rulers in check.
"If this council does not meet our aspirations and cannot serve our interests, we will never hesitate to have another revolution," said Ramzi al-Taqi, a fruit pedlar.
"We would topple the council just like we did the former regime," he said.
The transition's key documents were signed on Saturday at a ceremony attended by a host of foreign dignitaries, signalling that Sudan could be on its way to shedding its pariah status.
Task
Sudan's new rulers are expected to push for the lifting of the suspension from the African Union that followed a deadly crackdown on a sit-in in June. The ruling council will also seek to have the country removed from the US list of state sponsors of terrorism.
Bashir is wanted by the International Criminal Court in The Hague for his role in massacres in the Darfur region, where a rebellion broke out in 2003.
He appeared in court on Monday—but only on charges of corruption for the opening of a trial in which an investigator said the deposed leader admitted to receiving millions in cash from Saudi Arabia.
Pictures of the 75-year-old autocrat sitting in a cage during the hearing instantly became a symbol of his Islamist military regime's downfall.
The sight of their former tormentor in the dock was overwhelmingly welcomed by the Sudanese but many warned the graft trial should not distract from the more serious indictments he faces before the ICC.
"The evidence he committed genocide should come forward... Many civilians inside and outside Sudan have died because of him and he should face justice," one resident, Alhaj Adam, told AFP.
Sudan's transitional authorities would need to ratify the ICC's Rome Statute to allow for the transfer of the former military ruler to The Hague.
Amidst the euphoria celebrating the promise of civilian rule, unease was palpable within the protest camp that brought about one of the most significant moments in Sudan's modern history.
One reason is the omnipresence in the transition of Mohamed Hamdan Daglo, a member of the sovereign council and a paramilitary commander whose forces are blamed for the deadly repression of the protests.
His Rapid Support Forces sprang out of the Janjaweed militia notorious for alleged crimes in Darfur.
Pacifying a country still plagued by deadly unrest in the regions of Darfur, Kordofan and Blue Nile will be one of the most urgent tasks of Sudan's transitional institutions.
The other daunting challenge that awaits the fragile civilian-military alliance is the rescue of an economy that has all but collapsed in recent years.
It was the sudden tripling of bread prices in December 2018 that sparked the wave of protests fatal to Bashir's regime.