When the sovereign council is formed, the country's current ruling body, a transitional military council headed by General Abdel Fattah al-Burhan and his deputy, RSF commander General Mohamed Hamdan Dagalo, will be dissolved.
A governing body of six civilians and five generals will oversee a three-year transition period.
Months of unrest and deadly protests have followed the April overthrow of Sudan's former authoritarian President Omar al-Bashir after a mass popular uprising.
The prime minister will name a cabinet of 20 ministers from a list of nominees presented by the FFC, excluding the interior and defence ministers.
Media captionWhat happened during the 3 June massacre?
"We turned a tough page of Sudan's history by signing this agreement", Gen Dagolo, popularly known as Hemeti, told reporters.
The ceremony was greatly praised as representatives of both sides shook hands.
This is the first time the NCP has commented on developments in Sudan since Mr Bashir was ousted by the army in April following widespread protests.
The two sides had been divided over whether military leaders would be immune from prosecution over recent violence against protesters.
Image copyright EPA Image caption There have been protests on the streets of Sudan for months What does the declaration say?
The United Arab Emirates has welcomed the signing of a constitutional declaration between the military and main opposition coalition in the brotherly nation of Sudan.
Regarding external relations, the document stipulated setting up a balanced foreign policy while preserving the country's sovereignty, security and borders.
The country's prime minister will be appointed with the approval of the council on August 20, and he will be sworn in in front of the council and head of the supreme court on August 21.
The next day, the generals and protest leaders are to announce the composition of the new transitional civilian-majority ruling council, he said.
The arrangement on the affirmation came after the military gathering reported that nine RSF fighters had been expelled and confined in association with the murdering of nonconformists, including four schoolchildren, this week.
"Today, the civilian state is achieved", said Nusseibeh Abdullah, a 21-year-old woman.
Omar Hussein, a protester waving the Sudanese flag outside the negotiations hall, was overjoyed by the signing.
The military and protesters have reached several agreements, with each side fleshing out new details as they try to overcome suspicion and build a working relationship.