Gen. Abdel Fattah Al-Burhan appeared with Hamdok at a signing ceremony in the Presidential Palace, according to a live video broadcast on state television.
The deal agreed upon by Hamdok and Al-Burhan also includes the release of political detainees who were jailed following the October 25 coup, according to Mudawi Ibrahim, a prominent official in the National Forces Initiative, which helped mediate the talks.
Hamdok becomes leader again of the transitional government, which was first established following the ousting of former strongman and President Omar al-Bashir in 2019. Hamdok and Al-Burhan also agreed on a power-sharing deal between civilian and military leadership, but it will include as-of-yet unspecified restructuring, according to Ibrahim.
Ibrahim said Hamdok's agreement with Al-Burhan includes the following measures:
Gen. Burhan would restore the Council of Ministers which was dissolved following the October 25 coup.
Political detainees jailed after the takeover (including government, politicians and protesters) would be released.
A unified army would be created.
A committee is to be formed to investigate protests following the October 25 coup.
Sudan's constitution would be amended to include new articles to specifically outline the partnership between civilians and the military in the transitional government.
Hamdok was released on Sunday from house arrest, under which he had been placed following the coup, according to a source within the National Forces Initiative. An eyewitness said security forces surrounding Hamdok's residence since last month were withdrawn, but his personal guard remains in place.
The deal has met with resistance in Sudan. Police fired tear gas at a large group of protesters near the Presidential Palace in Khartoum on Sunday, according to eyewitnesses on the ground. The protests began in downtown Khartoum then moved on to the Presidential Palace in the city center.
Reacting to reports on the deal, the Darfur Lawyer's Association said in a statement: "There is no bargaining again" and "the solution starts with holding Al-Burhan accountable for the crimes committed since October 25, 2021."
"The Association assures that any initiative or bargaining for a settlement between yesterday's parties to bring Hamdok or others (like him) back in to power will 'not bring any result' when the demands and rights of the people of Sudan are not met," the statement added.
The deal was rejected by Sudan's Forces of Freedom and Change coalition (FCC), which said Sunday there is "no negotiation, no partnership, nor legitimacy for the coup plotters."
They also said the crimes of the regime -- from dissolving the constitution to causing repression of and violence against the people -- must be brought to trial in order that justice be met. The FCC outlined further allegations against the military in its statements, to which the military has not directly responded.
"We have nothing to do in any agreement with this brutal gang, and we are working with all peaceful means to bring this (gang) down, working with all the forces of the revolution, professional groups, resistance committees, and all the honorable people," the FCC statement said.
The statement closed by calling for a "new and glorious revolution," that will "tighten the noose on those behind the coup, and lead to their downfall."
The Sudan Doctors Syndicate (SDS) also rebuffed news of the political agreement reached by Sudan's military and Hamdok.
"News is circulating about an initiative that is being announced in which a political settlement is being announced," the SDS said in a statement.
The SDS added: "Whether it is true or not, we, the Sudan Doctors Legitimate Syndicate declare:
The blood of the martyrs still irrigates the streets and has not dried up
#Revolution is a people's revolution."
Sudan descended into a crisis last month, after the military dissolved the country's power-sharing government and declared a state of emergency.
The move sparked protests and condemnation of the military.