Droupadi Murmu was administered the oath of office by Chief Justice of India NV Ramana.
Odisha Chief Minister Naveen Patnaik, Lok Sabha Speaker Om Birla and MPs from all parties also attended the event.
President Murmu said, "My election is proof that the poor in the country can have dreams and also fulfil them."
She said getting a primary education was a dream for her and added that she would focus on welfare of the marginalised.
Earlier in the day, she visited Raj Ghat and paid her respects to Mahatma Gandhi. She then met outgoing President Ram Nath Kovind.
Murmu scripted history after defeating opposition's candidate Yashwant Sinha to become the first tribal woman to hold the top constitutional post.
President Murmu was born into a Santhali family. Santhals are one of the largest tribes mostly settled in West Bengal, Odisha and Jharkhand.
Before entering politics, Murmu worked as a junior assistant in the Irrigation Department of Odisha.