In an inauguration ceremony with low-key attendance by Western allies concerned by a crackdown on dissent, the former army chief called for hard work and the development of freedom "in a responsible framework away from chaos".
Last month's election, which officials said Abdel Fattah el-Sisi won with 97 percent of the vote, followed three years of upheaval since a popular uprising ended 30 years of rule by former air force commander Hosni Mubarak.
Security in Cairo was extra tight, with armoured personnel carriers and tanks positioned in strategic locations. Sisi said combating terrorism would be his top priority for the time being, a reference to Islamist foes he describes as a threat to national security.
"As for those who shed the blood of the innocents, there will be no place for them in this path," Sisi said in his first speech to the nation.
"And I say it loud and clear, there will be no soft stand with anyone who resorts to violence or whoever wants to delay our march towards the future that we want for our children."
Sisi toppled President Mohamed Mursi of the Brotherhood last July after mass protests against his rule.
Security forces then killed hundreds of Brotherhood supporters in the streets and jailed thousands of others in a crackdown that polarised the biggest Arab state, which controls the strategic Suez Canal and has a peace treaty with Israel.
In an earlier speech to foreign dignitaries, Sisi called for "an inclusive national march" in an apparent bid to heal political divisions and put an end to street protests that have hammered the economy.
Critics fear Sisi will become yet another authoritarian leader who will preserve the interests of the military and the Mubarak-era establishment, crushing the hopes of democracy.
Near Tahrir Square, the symbolic heart of the revolt against Mubarak where protesters now rarely tread, young men sold t-shirts with the image of Sisi in his trademark dark sunglasses.
Commentators on state and private media heaped praise on him, turning a blind eye to what human rights groups say are widespread abuses, in the hope that he can deliver stability and rescue state finances.
Many Egyptians share that hope, but they have limited patience, staging street demonstrations that toppled two leaders in the past three years, and the election turnout of just 47 percent shows Sisi is not as popular as when he toppled Mursi.
"Sisi has to do something in his first 100 days, people will watch closely and there might be another revolution. That's what people are like in this country," said theology student Israa Youssef, 21.
Western countries, who hoped the overthrow of Mubarak in 2011 would usher in a new era of democracy, have watched Egypt's political transition stumble.
Mursi was the country's first freely elected president, but his year in power was tarnished by accusations that he usurped power, imposed the Brotherhood's views on Islam and mismanaged the economy, allegations he denied.
Mursi's ouster was applauded by Egypt's Gulf Arab allies, who were alarmed by the rise of the Brotherhood, the international standard-bearer of mainstream Sunni political Islam.
The 86-year-old movement with branches in many countries, is seen as a threat to Gulf dynasties.
Saudi Arabia, the United Arab Emirates and Kuwait extended a lifeline exceeding $12 billion in cash and petroleum products to help Egypt stave off economic collapse after Sisi appeared on television and announced that the Brotherhood was finished.
King Abdullah of Saudi Arabia urged Egyptians this week to back Sisi and said they should disown "the strange chaos" of the Arab uprisings.
Kuwait's Emir, the King of Bahrain, the Crown Princes of Saudi Arabia and Abu Dhabi are attending Sisi's inauguration, according to a list provided by the Egyptian presidency.
In contrast, the United States only sent a senior advisor to Secretary of State John Kerry and most European countries only planned to send ambassadors.
"Just having ambassadors shows very clearly that while the governments are recognising the new transfer of power they are certainly not doing so with a huge amount of enthusiasm," said H.A. Hellyer, non-resident fellow at the Brookings Institution in Washington.
Diplomatic manoeuvrings pale as a problem for Sisi compared with an urgent need to fix state finances and tackle an Islamist insurgency to lure back tourists and investors.
The economy is suffering from corruption, bureaucracy and a widening budget deficit aggravated by fuel subsidies that cost nearly $19 billion a year.
Officials forecast economic growth at just 3.2 percent in the fiscal year that begins July 1, well below levels needed to create enough jobs for a rapidly growing population and ease widespread poverty.
Child nursery employee Kamal Mahmoud, 25, said he was optimistic but would give Sisi only two years to bring change.
If he doesn't succeed "he has no right to hold that position and he should join the others sitting in prison", he said.
Sisi has no strong political opponents, with the Brotherhood forced underground.
Parliamentary elections are expected later this year, but government opponents have been crushed and political parties weakened. Only one other candidate contested the presidential election. The military is unlikely to turn against Sisi unless mass street protests erupt.
"Sisi was the best option we had, so even if I still have worries about his stand on freedoms and even if he lets Mubarak's people come back, he is still the best candidate for now," said Mohamed Ahmed, an employee in a private firm.
The world knew little of Sisi before he appeared on television on July 3 to announce the removal of Mursi after vast crowds demanded he resign, and to promise democracy.
Sisi had kept a low profile as Mubarak's head of military intelligence. That approach dates back to his childhood in the run-down Cairo neighbourhood of Gamaliya.
While most boys played along alleys, Sisi kept to himself, focusing on his studies, working in his father's shop after school and weightlifting, people who knew him say.
But Sisi will need more than iron discipline to come up with solutions for Egyptians like Fathi Bayoumi, 60, who had hoped the 2011 revolt would ease hardships in his slum, where there are puddles of open sewage.
"He will do his best but it is not in his hands because the country has fallen. He does not have a magic wand May God be with him," said Bayoumi.
Poverty is just one of the challenges facing Sisi. He is likely to face the same protracted challenge from Islamists as his predecessors.
The Brotherhood has been declared a terrorist group and weakened but it has survived repression before.
"Sisi does not enjoy legitimacy or support from the people," said Mursi supporter Wael Kamel, a physician who lives in the town of Fayoum, south of Cairo. "The election was a farce."
Radical Islamist groups, who have threatened to bomb their way into power, have proven resilient despite army offensives.
Militants based in the Sinai Peninsula have stepped up attacks on police and soldiers since Mursi's ouster, killing hundreds. Other militants operating along the border with chaotic Libya are now seen by Sisi as a major threat.