BSMMU Director Brig Gen Abdul Majid Bhuiyan told the media at 11:53pm on Thursday that the former Jamaat-e-Islami chief died at 10:10pm.
"Process of handing over his body to his family will start tonight," said the director.
Later, a jail official told bdnews24.com that the body had been handed to them. "The body is with us," said jailer Mohammad Nesar Alam of Dhaka Central Jail. "The body will be sent to Dhaka Medical College and Hospital for autopsy after an inquest."
"Then the body will be given to his family."
Police started writing the inquest report in the early hours of Friday in presence of magistrate Tarik Hasan that finished around 3am. The body was then kept at DMCH morgue for autopsy.
The 92-year-old, who was sentenced to 90 years in jail for his crimes against humanity committed during the 1971 Liberation War, had been kept on life support since 9:30pm, Bhuiyan had earlier told bdnews24.com.
"He suffered a heart attack," BSMMU Vice-Chancellor Professor Pran Gopal Datta told bdnews24.com's Nurul Islam Hasib when Azam was put on life support.
The director's announcement followed another official's statement on live TV at 11:05pm that the convict "is still alive and being given respiratory support as part of usual treatment" amid speculations about his condition.
Later, the director emerged before the media to announce Azam's death. He said the former Jamaat supremo had died "within about half an hour of him being put on life support system".
Azam is the second war crimes convict to die in the hospital's prison cell after Joypurhat's Abdul Alim, a minister in the late 1970s in Gen Ziaur Rahman cabinet. BNP's Alim was to spend "the rest of his life in jail".
Azam's appeal hearing was slated for Dec 2 and is now sure to be declared "defunct" as it happened in case of Alim's.