His body was today flown by an Air Force helicopter to Guwahati in Assam from where it will be taken to Delhi. Prime Minister Narendra Modi will be present at the Delhi airport to receive his body.
The former President, who was in office from 2002 to 2007, had collapsed during the lecture at the Indian Institute of Management, Shillong, around 6.30 pm. He was taken to the Bethany hospital. Doctors said he had suffered a massive cardiac arrest.
"President Kalam was brought to the hospital at 7 pm. When he brought in there was no sign of life. He was taken to ICU to try and revive him, which was futile," hospital sources told NDTV.
The government has declared a seven-day national mourning as a mark of respect for the former President.
Paying a special tribute to Dr Kalam on Monday evening, PM Modi had said, "My mind is filled with so many memories, so many interactions with him. Always marvelled at his intellect, learnt so much from him."
Home Minister Rajnath Singh tweeted, "Deeply saddened at the sudden demise of the former president of India Dr. APJ Abdul Kalam. He was an inspiration to an entire generation."
The death of Dr. Kalam is an irreparable loss to this nation. He has left a big void hard to fill. I deeply mourn his death. RIP Kalam SahabRajnath Singh (@BJPRajnathSingh) July 27, 2015
Messages of condolence also poured in from various leaders.
Known as the Missile Man of India, Dr Kalam played a pivotal role in the Pokhran-II nuclear test in 1998. One of the most loved Presidents, he was also known as the People's President. While in his 70s, he was nominated for the MTV Youth Icon of the Year award in 2003 and in 2006.
He was awarded the Padma Bhushan and Bharat Ratna for his achievements.
Dr Kalam was born in Rameswaram on October 15, 1931, to a humble family. His father was a boatman.
A bright student, his interest in flying led to a degree in aeronautical engineering, and eventually to supervising the development of India's guided missile programme.
He was also the author of 10 books. His autobiography, Wings of Fire, written in 1999, had been a best seller.
Dr Kalam's last tweet, posted on Monday morning, read:
Going to Shillong.. to take course on Livable Planet earth at iim. With @srijanpalsingh and Sharma.- APJ Abdul Kalam (@APJAbdulKalam) July 27, 2015