Vice President M Venkaiah Naidu and Prime Minister Narendra Modi wished him on his birthday.
"His phenomenal as well as visionary leadership made India more developed and further raised our prestige at the world stage. I pray for his good health," PM Modi tweeted.
Wishing him on his birthday, Vice President Naidu posted a poem by Mr Vajpayee which urged people to remain united and not to give up hope in tough times.
Born in 1924, he entered politics during the Quit India movement in 1942. He was also the first external affairs minister to deliver a speech in the UN Assembly in Hindi.