The interview will be telecasted on National Geographic channel on Saturday at 10pm.
Modi sat down for an interview with Letterman to discuss India's vision to help fight climate change.
"If the world helps me with technology, helps me with resources, I will be the very first person to switch over to clean energy completely," says Modi in the interview with Letterman.
The interview is part of the Emmy award-winning documentary series "Years of Living Dangerously".
Modi's interview will be the first episode of the programme where Letterman will also meet other key government officials, along with travelling to rural villages where 300 million people live without power, to understand whether India will continue to use dirty fossils fuels like coal, or will it be able to lead the way with the renewable energy program.
The series investigates both the global and individual devastation wrought by climate change and features popular celebrity hosts including Harrison Ford and Matt Damon.
After conducting the interview, Letterman said, "I don't know what that was, but thank you. It's one of those things that I would like to do again. I was hoping he would ask me to sleep over. I have nothing but questions for this man."
This is what fans of Modi are tweeting about the interview: