Asahara, who had suffered partial blindness since childhood, was detained in May 1995, two months after the nerve agent attack on March 20, 1995, which killed 13 people and injured more than 6,000.
Japanese media reports say Asahara, who has been on death row for masterminding the 1995 deadly Tokyo subway gassing and other crimes, has been executed.
Scores of Aum members have faced trial over the attack - 13 were sentenced to death, including Asahara. A further six cult members remain on death row.
Yuji Ogawara, who heads a lawyers' group against the death penalty at the Japan Federation of Bar Associations, said the executions do not bring closure to Aum's crimes.
"Their death penalties had been finalized after sufficient deliberations at courts", Justice Minister Yoko Kamikawa said at a press conference in the afternoon, adding that she made careful considerations before ordering the executions on Tuesday.
"As I also bear a heavy responsibility, I would like to apologize to the victims", he said, although adding, "I have left Aleph more than 10 years ago, and I don't have any special feelings (for Asahara)".
AUM Shinrikyo renamed itself Aleph in January 2000.
Tomomasa Nakagawa, a doctor also executed Friday, and several other cultists broke into the Sakamotos' apartment late at night, strangled them to death and buried them in the mountains.
A riot police officer stands guard outside the Aum Shinrikyo cult headquarters 6th compound as the raids continued on 11 May 1995, searching for the mastermind behind the attacks.
The reverberations in Japan of an internal religious cult that utilized terrorism and fear remains in the memory today, just like the brutal events of the Tokyo Sarin attack in 1995. The sarin gas attack also shattered Japan's public safety image.
Even before the attack, in 1989, lawyer Tsutsumi Sakamoto, who opposed the cult, his wife and baby boy were murdered by cult members.
Asahara pleaded not guilty and never testified, only muttering and making incoherent remarks in court during the eight years of his trial, according to Reuters.
The group gradually became a paranoid doomsday cult, convinced the world was about to end in a global war and that only they would survive. "I hope they will not launch terror attacks", like the 1994 sarin gas attack in Matsumoto, Nagano Prefecture that killed eight people.
Born Chizuo Matsumoto in 1955 on the southwestern island of Kyushu, Asahara changed his name in the 1980s, when the Aum cult was being developed. At its peak, Asahara had tens of thousands of followers worldwide.
In 2016, police in Russian Federation conducted a number of raids on suspected cult members in Moscow and St Petersburg.