Journalist Jamal Khashoggi was killed in a fight in the Saudi consulate in Istanbul, the country's state TV reports, quoting an initial inquiry.
Deputy intelligence chief Ahmad al-Assiri and Saud al-Qahtani, senior aide to Crown Prince Mohammed Bin Salman, were sacked over the affair, it says.
US President Donald Trump said what had happened was "unacceptable" but added that Saudi Arabia was a "great ally".
This is the first time the kingdom has admitted Mr Khashoggi is dead.
The acknowledgement follows two weeks of denials that Saudi Arabia had any involvement in the disappearance of the prominent Saudi critic when he entered the consulate in Istanbul on 2 October to seek paperwork for his forthcoming marriage.
The Saudi kingdom had come under increased pressure to explain Mr Khashoggi's disappearance after Turkish officials said he had been deliberately killed inside the consulate, and his body dismembered.
On Friday, Turkish police widened their search from the consulate grounds to a nearby forest where unnamed officials believe his body may have been disposed of.
Observers are questioning whether Riyadh's Western allies will find the Saudis' account of a "botched rendition" convincing - and whether it will persuade them not to take punitive action against Saudi Arabia.
The UK Foreign Office said it was considering its next steps after hearing the report.
Only a first step
Analysis by BBC Security Correspondent Frank Gardner
The Saudi leadership will now be hoping that its belated admission that Khashoggi did die, after all, inside its consulate - coupled with a handful of sackings and arrests - will be enough to draw a line under this affair. It will not.
This is only a first step towards publicising the truth of what really happened. Given the days of indignant denials by the Saudi leadership it's doubtful we would have even got this far without sustained international pressure.
There can only be one of two possible alternatives here: either - as many suspect - the powerful Crown Prince Mohammed Bin Salman was to blame or he had lost control of his inner circle, something most observers find hard to believe.
MBS, as he is known, has a huge following amongst young patriotic Saudis who see him as a visionary reformer. If that support were now to ebb away then the crown prince could find himself dangerously isolated at court.
What is Saudi Arabia's version of events?
A statement from Saudi Arabia's public prosecutor says a fight broke out between Mr Khashoggi, who had fallen out of favour with the Saudi government, and people who met him in the consulate - ending with his death.
Investigations are still under way, it says, and 18 Saudi nationals have been arrested. The Saudi authorities have yet to give evidence to support this version of events.
Unnamed officials speaking to Reuters news agency and the New York Times say the Saudis did not know the whereabouts of the body after it was handed to a "local collaborator" to dispose of.
Who was sacked?
Saud al-Qahtani is a prominent member of the Saudi Royal Court and adviser to Prince Mohammed bin Salman.
Major-General Ahmed al-Assiri has acted as the top spokesman for the kingdom about the war in Yemen.
He spoke to the BBC in 2017 about the conflict, defending Saudi Arabia's actions.
King Salman has also reportedly ordered the formation of a ministerial committee, headed by Crown Prince Mohammed, to restructure the intelligence services.
Saudi Arabia says it acted on information provided by Turkish authorities as part of its inquiry, investigating a number of suspects.
How have Saudi's Western allies reacted?
US President Donald Trump said the arrests were an important "first step", and praised the kingdom for acting quickly. He said the official explanation was "credible", despite many US lawmakers expressing disbelief over the Saudi account.
He stressed the importance of Saudi Arabia as a counterbalance to Iran in the Middle East, and pushed back against the need for sanctions against the country in light of the new information, talking about the effect of such a move on the US economy.
Earlier this week President Trump had warned of "very severe" consequences if Saudi Arabic was proved to have killed the journalist.
A number of US lawmakers, including a Republican highly critical of the Saudis, Senator Lindsey Graham, said they were sceptical about the report on the journalist's death.
To say that I am skeptical of the new Saudi narrative about Mr. Khashoggi is an understatement. https://t.co/am4fraUL6H— Lindsey Graham (@LindseyGrahamSC) October 19, 2018
The UK Foreign Office described it as "a terrible act" and said the people behind the killing "must be held to account".
Turkey has vowed to reveal all of the details of the killing, according to a spokesman for the ruling Justice and Development party quoted by Anadolu news agency.
Meanwhile, Australia is the latest country to announce it is withdrawing from an investment summit in Saudi Arabia later this month - joining a growing boycott that includes the US, UK, Dutch and French finance ministers over the Khashoggi killing.
Dutch Prime Minister Mark Rutte has called for a "thorough investigation" to make sure "all relevant facts will be clear as soon as possible".
Mr Khashoggi's fiancée, Hatice Cengiz, questioned in a tweet what had happened to his body, saying: "The heart grieves, the eye tears, and with your separation we are saddened, my dear Jamal."
Why does Turkey say he was murdered?
Turkish officials believe Mr Khashoggi was killed by a team of Saudi agents inside the consulate, and his body then removed - and they say they have video and audio evidence to back this up.
Saudi Arabia has denied this, and initially insisted Mr Khashoggi had freely left the embassy.
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.
Turkish media said earlier this week they had identified a 15-member team of suspected Saudi agents who flew into and out of Istanbul on the day of the disappearance.
Jamal Khashoggi disappearance: The key events
- 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 believe 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
15 and 17-18 October
- 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