Journalist Jamal Khashoggi died after a fight in the Saudi consulate in Istanbul, the country's state TV reported quoting an initial probe.
It said deputy intelligence chief Ahmad al-Assiri and Saud al-Qahtani, senior aide to Crown Prince Mohammed Bin Salman, were dismissed over the affair.
The White House acknowledged the report, and said it would continue to "closely follow" all investigations.
This is the first time the kingdom has admitted Mr Khashoggi has died.
Saudi King Salman has also reportedly ordered the formation of a ministerial committee, headed by Crown Prince Mohammed, to restructure the intelligence services.
The journalist was last seen entering the Saudi consulate in Istanbul on 2 October, to pick up paperwork that would allow him to marry his fiancée Hatice Cengiz.
Reports on Saudi state media followed shortly after King Salman spoke on the phone to Turkey's President Recep Tayyip Erdogan about the case.
The pair exchanged information and agreed to continue cooperation in the investigation, Turkish presidential sources said.
Saudi Arabia reportedly acted on information provided by Turkish authorities as part of its inquiry, investigating a number of suspects.
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Earlier police in Turkey expanded their search for Mr Khashoggi's body, with unnamed officials saying his body may have been disposed of in the nearby Belgrad forest or on farmland.
Turkey alleges he was murdered in the consulate by a Saudi hit squad.
What did Saudi state media report?
A statement from Saudi Arabia's public prosecutor said a fight broke out between Mr Khashoggi and people who met him in the consulate - ending with his death.
"The investigations are still under way and 18 Saudi nationals have been arrested," the statement read.
Reports also spoke of the dismissal of the two senior officials.
Saud al-Qahtani is a prominent member of the Saudi Royal Court and adviser to Prince Mohammed bin Salman.
Image copyrightTWIITER/@SUADQ1978
Major-General Ahmed al-Assiri has acted as the top spokesman for the kingdom about the war in Yemen.
Gen Asiri spoke to the BBC in 2017 about the conflict, defending Saudi Arabia's actions.
What's been the reaction to the Saudi report?
The White House acknowledged the Saudi investigation in a statement shortly after the announcement.
"We will continue to follow the international investigations into this tragic incident and advocate for justice that is timely, transparent, and in accordance with all due process," the statement read.
The statement also offered "deepest condolences" to Mr Khashoggi's family, saying they were "deeply saddened" to hear confirmation of his death.
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New statement from the White House on Saudi Arabia acknowledging the death of Jamal Khashoggi
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US President Donald Trump earlier this week said there would be "very severe" consequences if Saudi Arabia was proved to have killed the journalist.
However, Mr Trump has also been accused of providing cover to the Saudi government.
He previously said he would not cancel military contracts with Saudi Arabia because "I don't want to hurt jobs", and also said he was unhappy Saudi Arabia was being treated as "guilty until proven innocent".
US Senator Lindsey Graham, a Republican highly critical of the Saudis, said he was "sceptical" of the report on the journalist's death.
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The incident has already caused considerable strain between Saudi Arabia and its Western allies, with several politicians pulling out of an investment conference - the so-called "Davos in the Desert" - scheduled for next week in Riyadh.
The Saudi crown prince is hosting the event to build support for his reform agenda.
However, a number of major businesses - including Pepsi and EDF - are still intending to go despite growing pressure for a boycott.
What happened to Jamal Khashoggi?
Mr Khashoggi - a prominent journalist who fell out of favour with the Saudi government - had been living in self-imposed exile in the US since last year.
He was last seen entering the Saudi consulate in Turkey's capital Istanbul on 2 October, to pick up paperwork that would allow him to marry his fiancée Hatice Cengiz.
Turkish officials believe Mr Khashoggi was killed by a team of Saudi agents inside the consulate, and his body then removed.
Saudi Arabia has denied the claims, and initially insisted Mr Khashoggi had freely left the embassy.
Why does Turkey say he was murdered?
Turkish officials say they have audio and video recordings that show Mr Khashoggi being murdered by a team of Saudi agents.
Turkish newspapers with close links to the government have published gruesome details of the alleged audio, including what they describe as the sounds of screams and Mr Khashoggi being interrogated and tortured.
Meanwhile, Turkish media say they have identified a 15-member team of suspected Saudi agents who flew into and out of Istanbul on the day of the disappearance.
Turkish officials say the group brought a bone saw into the country and that one of its members was a doctor who specialised in post-mortems.
Jamal Khashoggi disappearance: The key events
2 October- 03:28: A private jet carrying suspected Saudi agents arrives at Istanbul airport. A second joins it late afternoon
- 12:13: Several diplomatic vehicles are filmed arriving at the consulate, allegedly carrying some of the Saudi agents
- 13:14: Mr Khashoggi enters the building, where he is due to pick up paperwork ahead of his marriage
- 15:08: Vehicles leave the consulate and are filmed arriving at the nearby Saudi consul's residence
- 21:00: Both jets leave Turkey by 21:00
- Turkish government announces Mr Khashoggi is missing, thought to be in the consulate
- Saudi Arabia says he left the embassy
- Turkish officials tell the BBC they believed Mr Khashoggi was killed at the consulate. This is later strongly denied by Saudi Arabia
- Turkish officials tell BBC Arabic they have audio and video evidence of the killing. The existence of such tapes had previously been reported by local media
- Forensic teams carry out searches of consulate
- Saudi state TV reports an initial investigation shows Jamal Khashoggi died in the consulate
- Two Saudi senior officials are dismissed and King Salman announces the formation of a ministerial committee to restructure the intelligence services
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