But his victory claim was swiftly challenged by his rival, while shortly before the final result the generals who have run the country since the overthrow of Mubarak issued new rules that made clear real power remains with the army.
"Mohamed Morsy is the first popularly elected civilian president of Egypt," the official website of Brotherhood's Freedom and Justice Party announced.
But an aide to Morsy's opponent, former Prime Minister Ahmed Shafik, said the group was "hijacking the election."
"Our counting of the votes has so far showed that we are ahead with 52% of the vote but we refuse to break the law and issue any numbers now," said Mahmoud Baraka, spokesman for Shafik's campaign.
Egypt's state television reported both claims. The official election committee has yet to make any announcement.
The US-educated Morsy, in his first comments since the victory announcement, promised at a news conference to be president for all Egyptians and said he would not "seek revenge or settle scores."
"Thanks be to God who has guided Egypt's people to the path of freedom and democracy, uniting the Egyptians to a better future," Morsy said.
Hundreds of flag-waving young supporters of the Brotherhood gathered in Tahrir Square, where the anti-Mubarak revolution erupted 16 months ago. Outside the Brotherhood's Party headquarters, others danced and chanted: "Morsy Morsy ... the president." They also shouted "Down down with military rule."
A decree from the ruling military council, published as the count got under way on Sunday, spelled out only limited powers for the new head of state and reclaimed for itself the lawmaking prerogatives held by the Islamist-led parliament which the Supreme Council of the Armed Forces (SCAF) dissolved last week.
The order from Field Marshal Hussein Tantawi, the chairman to the Supreme Council, indicated that the army, which also controls swathes of Egypt's economy, has no intention of handing substantial power now to its old adversary the Brotherhood (see background).
"SCAF will carry legislative responsibilities ... until a new parliament is elected," the council's order said.
It raised a question of how, even if a civilian head of state is sworn in this week, Tantawi can claim to have met his own deadline of July 1 for relinquishing control - a deadline the armed forces' major patron and paymaster the United States had stressed in recent days it was expecting him to respect.
The Brotherhood has contested the army's power to dissolve parliament and warned of "dangerous days".
Liberal and Islamist opponents denounced the move as a "military coup".
The council's "constitutional declaration", issued under powers it took for itself after pushing aside Mubarak to appease street protests in 2011, was a blow to democracy, said many who aired their grievances on social media, a favoured weapon in the Arab Spring that ended Mubarak's 30-year rule.
"Grave setback for democracy and revolution," tweeted former UN diplomat and Nobel peace laureate Mohamed ElBaradei.
"SCAF retains legislative power, strips president of any authority over army and solidifies its control," he said.
"The 'unconstitutional declaration' continues an outright military coup," tweeted Abdel Moneim Abol Fotouh, a moderate Islamist knocked out in the first round of the presidential election last month. "We have a duty to confront it."
A Facebook page whose young activists helped launch the uprising mocked the army's order, noting Egypt would have a head of state with no control over his own armed forces: "It means the president is elected but has no power," one comment read.