The sarin gas subway attack killed 13 people and sickened more than 6,000. Japanese media reports Asahara, who has been on death row for masterminding the 1995 deadly Tokyo subway gassing and other crimes, has been executed.
Japan's public broadcaster NHK said six other former members of the cult who had been convicted of involvement in the attack had also been hanged shortly after Asahara, whose real name was Chizuo Matsumoto.
The group was also held responsible for an earlier sarin attack on June 27, 1994, in a parking lot near the houses of judges in Matsumoto, Nagano Prefecture, which killed eight people.
The relatives of those killed in the attack, and others who were injured welcomed the executions.
Japanese government spokesman Yoshihide Suga confirmed that Asahara was executed Friday.
The move drew sharp criticism from some lawmakers as well as Amnesty International, which called capital punishment "the ultimate denial of human rights".
"We should have heard more stories from the people involved and deepened discussions in society to get to the bottom as to why such crimes related to religion happened", Ogawara said.
The attacks left 13 dead and injured more than 6,000.
On 20 March 1995, cult members released the Sarin on the Tokyo subway.
Asahara and five of the six followers had been implicated in the subway attack.
In Japan, death sentences are not carried out until the verdict against all accused and accomplices are final, with no pending appeals left against any of the group.
He was sentenced to death in 2004, one of 13 cult members who ended up on death row and the first to be executed.
The Aum cult, now renamed Aleph, officially disowned Asahara in 2000, but it has never been banned and experts say the former guru retained a strong influence. At its peak, Asahara had tens of thousands of followers worldwide.
Aum Shinrikyo's killings began in November 1989, when lawyer Tsutsumi Sakamoto - who was working on a class action case against the cult - was brutally murdered along with his wife and child.
Following reports of the executions, Joyu reiterated his apology to people affected by AUM but said he is no longer part of the original cult.
"The fear, pain and sorrow of the victims, survivors and their families - because of the heinous cult crimes - must have been so severe, and that is beyond my imagination", Justice Minister Yoko Kamikawa told a news conference. But it gradually became a paranoid doomsday cult, convinced the world was about to end in a global war and that only they would survive, according to BBC News.
At its peak, the group had 10,000 members in Japan and 30,000 followers in Russian Federation, the Associated Press reports.