Modi paid floral tributes to Shastri at his samadhi Vijay Ghat, after visiting Mahatma Gandhi's memorial at Raj Ghat.
Shastri's birth anniversary coincides with that of the father of the nation Mahatma Gandhi.
Shastri, who was a Congress leader, served as the second Prime Minister of the country.
"A symbol of strong determination and simplicity who gave India the slogan of Jai Jawan, Jai Kisan- Lal Bahadur Shastri. I bow before him," Modi tweeted.