The Atyrau regional prosecutor's office announced on its website that the two bombs that exploded in the city center were detonated by a 23-year-old local resident, Bauyrzhan Qanatuly Sultanghaliev.
It said the bomber was identified by his relatives and through his fingerprints.
The statement also said investigators found materials and chemicals used to manufacture an explosive device in Sultanghaliev's apartment.
The Atyrau police have classified the bombings as a terrorist act using explosives. The first explosion took place at about 8:45 a.m. on Qulmanov Street, and the second around 9:50 a.m. in the central Saryarqa district.
Sultanghaliev died in the second blast. It is not clear whether he was planning to carry out a suicide-bomb attack or if he detonated the device by accident.
Meanwhile, "The Long War Journal," which monitors terrorist attacks around the world, reported on October 31 that a group called Jund al-Khilafah (Soldiers of the Caliphate), a "brigade" of foreign fighters based along the Afghan-Pakistani border, claimed credit for the Atyrau bombings in a statement released on jihadist forums.
In the statement, which has been translated by the SITE Intelligence Group, the group denied the operative killed was a suicide bomber and said the blasts "were just a warning to the government."
In a short video posted on the Internet last week, the same Islamist group demanded, in Russian, that Kazakhstan repeal a new law that bans daily Islamic prayers on the premises of government agencies.
In the video, one of the five masked fighters toting Kalashnikovs and a grenade launcher warned Kazakh President Nursultan Nazarbaev and the country's authorities they will take "appropriate measures" unless the law is repealed.
Bombing attacks are rare in Kazakhstan, but two explosions in May -- including the country's first-known suicide bombing -- killed at least two people.
Read more in Kazakh here and here