The executions went ahead despite heavy international pressure on Indonesia and President Joko Widodo to grant clemency.
Officials on Cilicap have yet to confirm the executions.
Attorney-General HM Prasetyo will make a media statement in Cilacap at 5.30am (local time), Cabinet Secretary, Andi Widjajanto said.
But Indonesian media has reported the eight were shot dead at 12.25am.
"We've carried out the executions," an Attorney General Office official, talking to the press on condition of anonymity, said, The Jakarta Post reported.
A Cilacap police officer told the Post: "The executions went well, without any disruptions."
Prayers were said for each of the eight, according to their respective religion, after the executions.
The others executed were Indonesian Zainal Abidin, Brazilian Rodrigo Gularte, Nigerians Sylvester Obiekwe Nwolise, Raheem Agbaje Salami and Okwudili Oyatanze, and Ghanaian Martin Anderson.
Mary Jane Fiesta Veloso of the Philippines was spared after a woman who allegedly recruited her to act as a drug courier gave himself up to police in the Philippines on Tuesday.
"There was a request from the Philippine president regarding the perpetrator who's suspected of committing human trafficking and surrendered in the Philippines," an attorney-general spokesman said in a text message.
"MJ is needed for her testimony."
Just hours before the scheduled executions, Australia, the European Union and France issued a statement calling on Joko to change his mind.
"In filing this petition, we ask Indonesia to reflect upon the impact on Indonesia's position in the world and its international reputation. We support Indonesia's efforts in obtaining clemency for its citizens abroad. Stopping this execution will help those efforts," the statement said.
"We fully respect the sovereignty of Indonesia. But we are against the death penalty in our country and abroad. The execution will not have a deterrent effect on drug-trafficking or stop others from becoming victims of drug abuse. Executing these prisoners now will not achieve anything."
On Monday, Joko told local media that the executions were a matter of law enforcement responding to a "drug emergency" in the country.
Chan, 31, and Sukumaran, 34, are the first Australians to be executed since December 2, 2005, when 25-year-old Melbourne man Van Tuong Nguyen was hanged in Singapore after being caught at Changi Airport with almost 400g of heroin.
The families spent their final hours with their loved ones on Nusakambangan on Tuesday before returning to the port town of Cilacap.
Andrew Chan's brother Michael had earlier tweeted: "Counting down the minutes until I loose a great Friend and Courageous brother.!! You will never be forgotten by so many".
Chan and Sukumaran were allowed to have their chosen spiritual guides with them in their last moments after Indonesian authorities had a change of heart.
Salvation Army minister David Soper and minister Christie Buckingham were to give Chan and Sukumaran solace and their last rites.
Australia's Consul General to Bali, Majell Hind, and lawyer Julian McMahon are also on Nusakambangan for official duties.
Ms Hind will receive the bodies of Chan and Sukumaran and take legal responsibility for them on the island.
They will be driven to Jakarta by local ambulance with an Australian consular officer following the execution.
The Australians' bodies will then be flown back to Sydney.
