They said that Guru was informed about his hanging late on Friday evening after a death warrant was issued by a Delhi court.
"He was told about his hanging yesterday (Friday) by the jailor," a source said.
The source said Guru was hanged about 20 metres from his cell where he spent 12 years in solitary confinement.
"He was happy and healthy before being hanged," said the jail's Director General Vimla Mehra.
"Before the hanging, a medical check-up was conducted on him. His health and blood pressure were normal," said Mehra.
"There were eight people, including a doctor, a magistrate and some jail officials, present when he was hanged. He was hanged for eight minutes," the source said.
Guru was buried quietly soon near his cell. After he was woken up at 5 am, he offered prayers before calmly approaching the noose, officials said.
A Muslim cleric was also present during his hanging.
Meanwhile, the family of Afzal Guru sought permission from jail authorities to perform his last rites in accordance with religious traditions.
In a letter to Mehra, drafted by Guru's lawyer ND Pancholi, wife Tabassum said the last rites of her husband should be performed in a dignified manner.
"If you could inform us when the family members can perform their 'Namaaz-e-Janaza', we would appreciate it," said the letter.
Guru was convicted for his role in plotting the December 13, 2001, attack on Parliament House, in which 10 people were killed when five armed terrorists stormed into the complex when 100 MPs, then prime minister Atal Bihari Vajpayee and his cabinet ministers were inside.