The former school teacher and state governor was elected to the largely ceremonial position last week with 64 percent of the vote by members of India's parliament and state assemblies.
"My election is proof of the fact that in India, the poor can dream and also fulfil those dreams," Madam President Murmu, who succeeds Ram Nath Kovind, said in Hindi after being sworn in by Chief Justice of India N V Ramana at Parliament's Central Hall.
Murmu, India's youngest president at 64 and the first to be born after Independence, took oath of office in the name of god to "preserve, protect and defend the Constitution and the law".
It is the power of India's democracy that a girl born in a poor tribal home could reach the topmost constitutional post, she said in her address, marking her journey from Odisha's Mayurbhanj district, one of the most underdeveloped in India, to the Rashtrapati Bhavan.
The country's deprived, poor, Dalits and tribals can see their reflection in her, a matter of immense satisfaction, she said and recalled her growing up years in a small tribal village where even getting primary education was like a dream.
Murmu, who was born in a Santhal family, went on to become the first person in the village to enrol for college education.
In her speech to the gathering, including Prime Minister Narendra Modi, ministers, former president Pratibha Patil, MPs as well as leaders such as Odisha Chief Minister Naveen Patnaik who backed her election, Murmu touched on various issues. These included the government's digital India and vocal for local' initiatives and its handling of the Covid pandemic.
She also paid tribute to India's freedom fighters, and said the country will have to move quickly on the twin tracks of sabka prayas' (everyone's effort) and sabka kartavya' (everyone's duty) to fulfil their expectations.
Murmu, who started public life as a councillor and was former Jharkhand governor, said she wanted to reassure all Indians, particularly the youth and women, that their interests will be supreme for her as president.
The prime minister described Murmu taking over as president as a watershed moment .
"In her address after taking oath, President Droupadi Murmu Ji gave a message of hope and compassion. She emphasised on India's accomplishments and presented a futuristic vision of the path ahead at a time when India is marking Azadi Ka Amrit Mahotsav," Modi said.
"The entire nation watched with pride as Smt. Droupadi Murmu Ji took oath as the President of India. Her assuming the Presidency is a watershed moment for India especially for the poor, marginalised and downtrodden. I wish her the very best for a fruitful Presidential tenure," he added.
The day, which started with outgoing president Kovind and Murmu arriving in a procession from the Rashtrapati Bhavan to the Parliament Building, was edged with ceremony and celebration.
India's new president was given a 21-gun salute after which she signed the oath register amid thunderous applause and thumping of desks.
After the short ceremony, Murmu and Kovind were escorted out of the Central Hall amid the roll of drums and blowing of trumpets.
There was a national salute by the President's Bodyguard at Gate No 5 of the Parliament, the new President and her predecessor left in a ceremonial procession back to the Rashtrapati Bhavan.
In keeping with the grand occasion, caparisoned horses, and men in white lined the route from Parliament up Raisina Hill to the British era presidential palace as the presidential convoy made its way slowly.
As monsoon clouds framed the dome of the Rashtrapati Bhavan, the new commander in chief of the armed forces inspected a tri-services guard of honour in the forecourt.
Former president Kovind and his family, who move to a bungalow in Lutyens Delhi, were given a formal send-off by the prime minister and other dignitaries as well as the Rashtrapati Bhavan staff.
Catapulted into the presidential spotlight, the unassuming Murmu is believed to be deeply spiritual and a keen practitioner of the meditation techniques of the Brahma Kumaris, a movement she embraced after she lost her husband, two sons, mother and brother in the just six years between 2009-2015.
Her daughter Itishree works in a bank in Odisha.
Her first steps in politics were taken in Rairangpur where she was elected as BJP councillor in the Rairangpur Notified Area Council in 1997. She rose to being a minister in Odisha's BJD-BJP coalition government from 2000 to 2004. In 2015, she was appointed governor of Jharkhand and stayed in the post till 2021.
Murmu had contested the 2014 assembly election from Rairangpur, but lost to the BJD candidate.
After completing her tenure as Jharkhand governor, Murmu devoted her time to meditation and social work in Rairangpur.
In tribute to her remarkable journey through personal tragedies and triumphs, there were celebrations in several places, including Ranchi and Bhubaneswar.