"It is with profound grief that we inform about the sad demise of Former Prime Minister of India, Shri Atal Bihari Vajpayee, at 05:05 PM," the AIIMS said in a statement.
It said his condition was stable for the last nine weeks, but "unfortunately, his condition deteriorated over the last 36 hours and he was put on life support systems."
"Despite the best of efforts, we have lost him today. We join the Nation in deeply mourning this great loss," said the statement by Dr (Prof) Aarti Vij.
Earlier today, Prime Minister Narendra Modi and a host of other BJP as well as opposition leaders drove to AIIMS as it became clear that the end was near.
"It was Atalji's exemplary leadership that set the foundations for prosperous and inclusive India in the 21st century," Modi said.
Vajpayee, who joined the Rastriya Swamsevak Sangha (RSS) in 1947 rose through ranks to become a stalwart of the BJP and was the first non-Congress prime minister to complete a full term in office.
"It was due to the perseverance and struggles of Atal Ji that the BJP was built brick by brick," Modi said in a tweet.
"He travelled across the length and breadth of India to spread the BJP's message, which led to the BJP becoming a strong force in our national
polity and in several states," he added.
Seen as a moderate face of BJP, Vajpayee's first became prime minister in 1996, leading a shaky coalition whose members were suspicious of the BJP's right-wing politics. It lasted for 13 days and collapsed after losing a vote of no-confidence.
His second stint as prime minister was in 1998 when the National
Democratic Alliance again came to power but that lasted for just 13 months.
Finally, the NDA with Vajpayee as PM returned to power in 1999 and was voted out in 2004.
A 10-time MP of the Lok Sabha, Vajpayee announced his retirement from politics in 2005. He was also a member of the Rajya Sabha twice.
The former prime minister was admitted to the hospital on June 11 with a kidney tract infection, urinary tract infection, low urine output and chest congestion.
Vajpayee, a diabetic, had only one functional kidney. He suffered a stroke in 2009 that weakened his cognitive abilities. Subsequently, he developed dementia.
Meanwhile, the government today announced seven-day state mourning as a mark of respect for former prime minister Atal Bihari Vajpayee who passed away today.
In a circular, the Home Ministry also said national
flag would be flown at half mast from today for seven days across India and a state funeral would be accorded to Vajpayee.
"As a mark of respect to the departed dignitary, it has been decided that seven days of state mourning will be observed throughout India from August 16-22, both days inclusive.
"During this period, the national flag will be flown at half mast throughout India where it is regularly flown and there will be no official entertainment during the period of the state mourning," the Home Ministry said.
The last rites of former prime minister Atal Bihari Vajpayee will take place at 4 pm tomorrow at Rashtriya Smriti Sthal here, BJP chief Amit Shah said.
The body of the BJP veteran has been kept at his official residence - 6 A Krishna Menon Marg. Shah said people can pay homage to the departed leader at his residence from 7.30 am to 8.30 am on Friday.
The body would then be taken to the BJP headquarters at Deen Dayal Upadhyay Marg at around 9 am, he told reporters.
The funeral procession would leave the BJP headquarters at 1 pm and the last rites would be performed at 4 pm, he said.
The national flag would also fly half mast on the day of the funeral in all Indian missions abroad.