It will cover more than 40 million families in rural and urban India - roughly a quarter of the population.
The "Saubhagya scheme" will largely be funded by the federal government.
The government also aims to provide free electricity to poor families identified by them based on socio-economic data.
It will bring "a monumental change in the lives of the poor", the PTI news agency quoted Mr Modi as saying on Monday.
About 300 million of India's 1.3 billion people are still not connected to the electricity distribution grid.