Friday's attack also wounded 227 worshippers in the first bombing of a mosque in the tiny Gulf state, and Kuwait's security services have vowed to catch and punish those responsible.
The Islamic State group's Saudi affiliate, the so-called Najd Province, claimed the bombing and identified the assailant as Abu Suleiman al-Muwahhid.
Kuwait's interior ministry gave the real name of the attacker as Fahd Suleiman Abdulmohsen al-Qaba'a, in a statement carried by the official KUNA news agency.
A handout photograph of Qaba'a showed a young bearded man wearing a traditional Saudi headdress.
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Earlier today, the ministry said that security services arrested the driver of the car that transported the bomber to the Al-Imam Al-Sadeq mosque in Kuwait City. He was named as Abdulrahman Sabah Eidan Saud and described as an "illegal resident" born in 1989.
Authorities yesterday arrested the car owner, Jarrah Nimr Mejbil Ghazi, born in 1988, and also listed as a stateless person.
Kuwait has also detained the owner of the house where the bomber was staying. He was described by the interior ministry as a Kuwaiti national who subscribes to "extremist and deviant ideology".
Alleged IS executioner Mohammed Emwazi, who became known by media as "Jihadi John", was born in Kuwait to a stateless family of Iraqi origin which later moved to London.
Local media said 18 of those killed were Kuwaitis, three Iranians, two Indians, one each from Pakistan and Saudi Arabia and one bidoon.
The breakthroughs in the bombing probe came a day after thousands of Kuwaitis braved scorching summer heat yesterday to attend the funerals of 18 victims.