Prosecutor Sheikh Saud al-Mojeb landed at Istanbul's Ataturk Airport on a private plane overnight, Anadolu added.
He is expected to meet with Istanbul chief prosecutor Irfan Fidan and visit the Saudi consulate where Khashoggi was killed.
The case has brought near unprecedented international scrutiny on Saudi Arabia, which is seeking to draw a line under the crisis after offering a series of differing narratives in the weeks following Khashoggi's murder.
The 59-year-old Washington Post contributor, who had criticised Saudi Arabia's powerful Crown Prince Mohammad bin Salman, vanished after entering the Saudi consulate on October 2 to obtain paperwork for his marriage to his Turkish fiancee.
Gruesome reports in the Turkish media have alleged he was killed and dismembered by a team sent from Saudi Arabia to silence him.
US Defence Secretary Jim Mattis said Sunday that Saudi Foreign Minister Adel al-Jubeir had vowed Riyadh would conduct a "full" investigation .
"We discussed it... the need of transparency, full and complete investigation . Full agreement from FM Jubeir, no reservations at all," Mattis said following talks in Bahrain.
He added he was confident that the Saudi investigation would include Turkey's findings.
"Certainly Turkey with the evidence that they have compiled will ensure that there is more than one review of what is going on there and I am certain the investigation will include the evidence that Turkey has put forward so far," Mattis said.