A large number of Indian-Americans are disappointed by not being able to get tickets of the visitor's gallery for the event.
Indian-Americans from across the US are flying to Washington DC to listen Modi in person.
"It's a dream come true," Chicago-based Bharat Barai said.
"I am sure after listening to him, people of this country and Congressmen would realise the importance Modi attaches to the India-US relationship," he said.
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Rangaswami, the founder of Indiaspora, is among the lucky few who have managed to get a ticket to the visitors' gallery of the House Chambers, which has limited number of seats.
Congressional sources told PTI that lawmakers are having a tough time in declining requests for a ticket to the joint address by Modi.
In fact, most of the Congressmen have been allocated one ticket each.
The speech would be telecast nationwide live on C-Span, a cable and satellite television network.
"The invitation (to the Prime Minister) itself shows the status of the relationship and how far we have come," Swadesh Chatterjee, an eminent Indian-American, said.
Chatterjee, who played a key role in reviving the India-US relationship after the Pokhran nuclear tests, vividly remembers how he and many other Indian-Americans had to lobby for months in the Congress to invite the then Prime Minister Atal Bihari Vajpayee to address a joint session of the Congress on September 14, 2000.
Prime Minister Modi about growing US-India ties and the numerous ways the two countries can deepen their strategic partnership even further," said Ronak D Desai, an international Security Fellow at New America and an Affiliate at the Belfer Center's India and South Asia Programme at Harvard University.
"Lawmakers are eager to hear from Prime Minister Modi about the ways the United States and India can collaborate together to be a force of global and regional stability and deepen their cooperation even further. The partnership enjoys rare bipartisan support, and the us will continue to play a central role in moving it forward in a host of key arenas," Desai said.
Manmohan Singh was the last Indian Prime Minister to address a joint meeting of the Congress on July 19, 2005.
Earlier addresses have been by Atal Bihari Vajpayee (September 14, 2000), P V Narasimha Rao (May 18, 1994) and Rajiv Gandhi (July 13, 1985).
Modi's engagement at the US Capitol on June 8 is expected to be kicked off by a meeting with the top leaders of the Congress including House Speaker, Paul Ryan; House Minority Leader, Nancy Pelosi; Senate Majority Leader, Mitch McConnell and Senate Minority Leader Harry Reid.
Soon after the joint address, Ryan would host a lunch for the Prime Minister at the Capitol. This will be attended by top Congressmen.
After lunch, the Prime Minister would attend a reception jointly hosted by the Senate Foreign Relations Committee and House Committee on Foreign Affairs in association with the House Caucus for India and Indian Americans and the Senate India Caucus.