He became Asia's first Nobel laureate after winning the Nobel Prize in literature for Gitanjali in 1913.
Two of his songs are now the national anthems of Bangladesh and India.
Tagore wrote novels, short stories, songs, dance-dramas, and essays on political and personal topics. Gitanjali, Gora, and Ghare-Baire, Chokher Bali are among his best-known works.
President Abdul Hamid and prime minister Sheikh Hasina issued separate messages on the occasion.
Bangladesh Television and other private television channels and Bangladesh Betar will air special programmes highlighting the life and works of Rabindranath.