Moving to quell fears of how an Islamist organisation would handle the reins of power, the Muslim Brotherhood politician pledged to respect the constitution and the rule of law and protect the people of Egypt, after taking the oath before the Supreme Constitutional Court.
However, the threat of a power struggle between the party and the army still hangs in the air.
"We aspire to a better tomorrow," he said during the ceremony, broadcast live on state television. "Today, the Egyptian people laid the foundation of a new life – absolute freedom, a genuine democracy and stability."
Mursi, a 60-year-old US-trained engineer, is the first president since the king was toppled by army officers in 1952 not to have been drawn from top military ranks.
His victory marked a dramatic reversal of fortunes for the Muslim Brotherhood, Egypt's oldest Islamist movement, which was banned in the country for decades.
Following the ceremony, he travelled to Cairo University to make his inauguration address and was given an official welcome by an army band that played the national anthem as he stood to attention. Military ruler Field Marshal Hussein Tantawi was in attendance.
Mursi earlier took a symbolic oath of office before crowds in Cairo's Tahrir Square – the birthplace of the uprising that ended former president Hosni Mubarak's authoritarian rule last year.
He vowed to reclaim presidential powers stripped from his office by the military council that took over from the ousted leader.
Addressing the "Muslims and Christians of Egypt", he promised a "civil, nationalist, constitutional state", making no mention of the Brotherhood's dream of creating an Islamic state.
"There is no power above people power," he said told the crowds. "Today, you are the source of this power."
He added: "The revolution must continue until all its objectives are met."
His defiant speech was a clear challenge to the army, which also says it embodies the will of the people and sees itself as the guarantor of national interests and the state.
The military's insistence that Mursi take his oath before the constitutional court – and his riposte in Tahrir – sets the stage for a protracted struggle for power in Egypt.
Egypt remains in political limbo, without a constitution, a lower house of parliament or any clarity about the role of a military establishment anxious to stay in the driving seat.
Under the military council's rule, Egypt has experienced a bumpy and sometimes violent transition in which parliamentary and presidential elections have been held, without setting the country on a clear path to democracy or constitutional rule.
An assembly that is supposed to write a new constitution has begun work after its predecessor fell apart amid disputes over whether Islamists were over-represented in a country with a 10% Christian minority and many secular-minded liberals.
Egypt is also more polarised than ever. Mursi narrowly won a run-off vote last month against Ahmed Shafik, a former air force chief and Mubarak's last prime minister. However, many voters were dismayed at being given the choice of either an Islamist or a man seen as a remnant of Mubarak's era.
Mubarak was jailed for life last month for his part in the killing of protesters during the revolution in 2011.
The military, the source of every previous president in the Arab republic's 60-year history, also runs business enterprises accounting for an estimated one-third of the country's economy.
It does not intend to jeopardise the $1.3 billion (£800m) a year it receives in military aid from the United States to back Egypt's 1979 peace treaty with Israel, widely criticised by Islamists.
Mursi has said he will respect Egypt's international obligations and does not want to take the country back to war.
With his speech in Tahrir, he appeared to signal a determination to use popular legitimacy to defeat entrenched military power.
"Say it loud, Egyptians: Mursi is the president of the republic," the crowd chanted. "A full revolution or nothing. Down with military rule. We, the people, are the red line."