The 64-year-old lawmaker from the Congress party, whose coalition government was returned to power after last month's elections, will hold the country's top Constitutional post, the Press Trust of India reported. She was elected unopposed.
A resolution in parliament naming her speaker, which was moved by Sonia Gandhi, president of the Congress-led coalition, was approved by a voice vote in the lower house of parliament. Leaders of all major opposition parties also had similar motions proposing her name for the post.
Kumar, a member of the Dalit community, is a former Indian Foreign Service officer and also had been a federal minister.
Indian Prime Minister Manmohan Singh, who belongs to the minority Sikh community, said Kumar's selection is a historic moment for the country, and praised her service as a distinguished diplomat and 25 years in parliament, PTI reported.
Kumar said she would make every effort to ensure the dignity of the lower house and its members.
She is the daughter of the late Jagjivan Ram, a former deputy prime minister of India.
India already has a woman President.