Taking his oath, the 73-year-old BJP leader said he would "do right to all manner of people without affection or ill-will".
Speaking as he was sworn in by President Draupadi Murmu, Mr Modi said he would uphold the sovereignty and integrity of India and govern with "true faith and allegiance to the constitution".
"I will do right to all manner of people in accordance with the constitution and the law without fear or favour," he said. A council of ministers of Mr Modi’s new cabinet were also sworn in during the ceremony.
He is only the second Indian leader to win a third consecutive term after the country’s first prime minister, Jawaharlal Nehru. Exit polls had projected outright victory for his Hindu Nationalist BJP party, which ruled India for a decade, but it lost its parliamentary majority in the general election.
His NDA bloc relied on two key allies, the Telugu Desam Party (TDP) and the Janata Dal (United) JD(U), to cross the 272-seat mark needed to form the government.
BJP-led National Democratic Alliance won the general election with 293 seats, a much lower margin than predicted by exit polls. The election saw a resurgence of India’s opposition, which won 234 seats.
Thousands of guests attended the inauguration at Delhi's presidential palace. Among them were the heads of neighbouring Bangladesh, Nepal, Sri Lanka, and the Maldives - but not Pakistan or China.
Tight security was in place in Delhi, which was declared a no-fly zone, with more than 2,500 police officers deployed around the venue.
On Friday, the elected MPs voted Mr Modi as the leader of the Lok Sabha (the lower house of the parliament), leader of the BJP parliamentary party, and leader of the NDA.
It is not clear what concessions his allies may have negotiated in return for their support. India media report that several are seeking key ministerial posts.
The opposition INDIA alliance, led by the Congress party, has called the election a mandate against Mr Modi's government.
Mr Modi, however, countered this on Friday, saying: "Opposition tried to paint 2024 Lok Sabha results as a loss for us. But we didn’t lose, we never lost, we will never lose."
Mr Modi thanked voters for their mandate, and said he would "do everything" to eradicate corruption and poverty.
"Empowering the poor and middle class is our priority," he said.
During his election campaign, Mr Modi and his party were accused by critics of using hate speech, attacking the country's Muslim minority, and jailing opposition figures.
On Friday, the prime minister-elect said the NDA alliance was "committed to the principle of "sarva panth sambhava" (religious equality).
The INDIA alliance has said it will fulfil its duty in parliament by holding the government in check and protecting the constitution.
