In a message, Modi said: "His prose and poetry have influenced generations. He represents the best of modern and ancient Indian intellectual thought."
He said: "Gurudev Tagore blended the wisdom of India's past with the promise of its future through his literature, art and music."
The prime minister also said that "he taught us the power of free thinking while inspiring us to dream of a 'Heaven of Freedom' where the mind is without fear and the head can he held high".
"We proudly remember Gurudev Tagore's immense contribution in the making of our nation," he added.
In 1913, Tagore became the first Indian to win the Nobel Prize in Literature. He is the composer of the country's national anthem.