The city will get Rs.572 crore for the project that aims at underground cabling of power lines, cutting line losses and many other things, officials said.
The prime minister said his government was committed to bringing power to every village and every household in India by 2022, when the nation celebrates the 75th year of attaining freedom.
Modi thanked the people of Varanasi and said he was indebted to them as it was because of them that he became a parliamentarian and then the prime minister.
He also launched seven other projects and schemes that include construction of a ring road in Varanasi city, beautification and widening and revamp of the road from Babatpur airport to the city.
Modi referred to the recent order of the Allahabad High Court in which it had quashed assimilation of 'shiksha mitra' as teachers in government schools.
He said he will definitely try and find a way to resolve the problem once the court order is received in writing.
"I am pained to hear that a 'shiksha mitra' committed suicide on hearing the court verdict," Modi said and urged the people not to take such drastic steps and instead be patient and let the government find a way.