Sudan's army ruler Abdel Fattah al-Burhan lauded the "long-awaited deal" in an interview on Saudi broadcaster Al-Hadath. Protests began last December when President Bashir imposed austerity measures to prevent an economic crisis.
In June, security forces violently dispersed the protesters' main sit-in outside the military headquarters in Khartoum, killing dozens of people.
Demonstrators have since called for authority to be transferred to a civilian administration.
The power-sharing deal envisages a governing body of six civilians and five generals.
Lebatt said that the delegations will continue talks on Saturday over the technical details of the signature procedures but did not elaborate further on the contents of the declaration.
"I am announcing to the Sudanese, African and global public opinion that the two delegations have fully agreed on the constitutional declaration", Mr Lebatt told reporters on Saturday.
The constitutional declaration is complementary to the power-sharing deal signed on 17 July, meant to form a joint civilian-military ruling body which will oversee the formation of a civilian parliament to govern for a three-year transition period.
The move against the paramilitary men of the feared Rapid Support Forces (RSF) stemmed from the fatal shooting of four schoolchildren and two other demonstrators during a rally against fuel and bread shortages in the city of Al-Obeid in North Kordofan on Monday.
"We do believe that tomorrow we will bring the Sudanese people good news about these talks", Ibrahim Alamin of the Forces for Freedom and Change (FFC) told a joint press conference early Friday after overnight talks with Sudan's Transitional Military Council (TMC).
The two sides had been divided over whether military leaders would be immune from prosecution over violence against protesters.
A sovereign council, cabinet and legislative body will be formed.
A general will head the council for the first 21 months, a civilian for the remaining 18.
The protest movement's legal affairs negotiator Ibtisam al-Sanhouri said the consitutional declaration sets the stage for a parliamentary system with a civilian prime minister. The military would select the defense and interior ministers during the transition.
Chairman of the Sudanese Congress Party Omer Al-Digair said in a statement that the constitutional declaration paves the way for establishing the transitional period institutions to assume the political, economic and social reform programs.
Demonstrators argue that Mr Bashir's regime is so deeply entrenched that it will take time to dismantle its political network and open the way for free and fair elections.