Mr Hamdok was quoted by Reuters news agency as saying he had agreed to the deal to stop the violence: “Sudanese blood is precious, let us stop the bloodshed and direct the youth’s energy into building and development.”
It is not clear how much power the reinstated prime minister and his cabinet of technocrats will have.
The military has come under intense international and domestic pressure to restore the transition to democracy. The World Bank froze its aid to Sudan, and the African Union (AU) suspended the country’s membership of the bloc.
The army entered into a fractious power-sharing arrangement with the FFC in August 2019, after long-time leader Omar al-Bashir was overthrown amid mass protests.
As part of that agreement, Gen Burhan had been due to step down as head of state, handing over to a civilian this month.
He says the army acted to prevent a civil war that was threatening to erupt because political groups had been inciting civilians against the security forces.
Mediators of the new agreement, which included academics, journalists and politicians, said the rules governing the transition towards democracy would be restored.
But questions are being asked about the military’s sincerity to do so, says BBC World Service Africa editor Mary Harper.
The fear is that continued instability in Sudan will further threaten the volatile Horn of Africa, she says.