Azam, who led the Jamaat-e-Islami during the 1971, died at the BSMMU on Thursday night after serving a year of his 90-year jail term for crimes against humanity.
Jailor Md Nesar Alam of the Dhaka Central Jail said the body was handed over at 7:20am on Friday morning after a post-mortem.
His family took his body to his Moghbazar residence.
Azam, the Jamaat ideological linchpin, had been kept at the BSMMU prison cell since his war crimes trial started in 2012.
Bangladesh's first war crimes tribunal sentenced him to 90 years in jail, considering his age and health, on July 15 last year.
Azam, the brain behind the conspiracy to thwart the birth of Bangladesh, had strongly backed a united Pakistan.
The war criminal, who never apologised or regretted going against the Bangalees, only served one year and three months for his war-time atrocities.
His family said he would be buried at their family graveyard at Moghbazar.
Abdullahil Azmi, his son, said the burial would take place after his other siblings returned from abroad.
Until then, Azam's body will be kept in a morgue.