According to the senior Saudi official, the Saudi team rolled up Khashoggi's body in a rug, took it out in a consular vehicle and handed it to a "local cooperator" for disposal.
One of the operatives then donned Khashoggi's clothes, eyeglasses and Apple watch and left through the back door of the consulate in an attempt to make it look like Khashoggi had walked out of the building, the senior Saudi official said.
Turkish investigators are likely to find out what happened to the corpse "before long", a senior Turkish official said earlier on Saturday.
Officials told Reuters in Turkey on Thursday that Khashoggi's remains may have been dumped in Belgrad Forest adjacent to Istanbul, and at a rural location near the city of Yalova, 90 km (55 miles) south of Istanbul,
Turkish sources say the authorities have an audio recording purportedly documenting Khashoggi's murder inside the consulate. Pro-government Turkish newspaper Yeni Safak, citing the audio, said his torturers cut off his fingers during an interrogation and later beheaded him.
Trump said no one from his administration has seen video or a transcript of what happened inside the consulate.
Khashoggi's Turkish fiancée, Hatice Cengiz, tweeted in Arabic: "They have taken your body from this world, but your beautiful smile will stay in my world forever."
Saudi Arabia had previously denied that Khashoggi died in the consulate.
But the Saudi public prosecutor said on Saturday that a fight broke out between Khashoggi and people who met him in the building, leading to his death. Eighteen Saudi nationals had been arrested, the prosecutor said.
Saudi state media said King Salman had ordered the dismissal of five officials, including Saud al-Qahtani, a royal court adviser seen as the right-hand man to Prince Mohammed, and deputy intelligence chief Ahmed Asiri.
The crisis prompted the king to intervene, five sources with links to the Saudi royal family told Reuters.
The king also ordered a restructuring of the intelligence service, to be led by Prince Mohammed, suggesting the prince still retained wide-ranging authority.
The dismissed official Qahtani, 40, rose to prominence after latching onto Prince Mohammed, becoming a rare confidant in his inner circle.
Sources say Qahtani would regularly speak on behalf of the crown prince and has given direct orders to senior officials including in the security apparatus.
The New York Times reported on Saturday, citing U.S. and Saudi officials, that Qahtani created the strategy behind the deployment an online army to harass Khashoggi and other critics of the kingdom on Twitter.
People close to Khashoggi and the government said Qahtani had tried to lure the journalist back to Saudi Arabia after he moved to Washington a year ago fearing reprisals for his views.
Asiri joined the Saudi military in 2002, according to Saudi media reports, serving as spokesman for a coalition backing Yemen's ousted president after Prince Mohammed took Saudi Arabia into that country's civil war in 2015. He was named deputy chief of foreign intelligence in 2017.
