The Saudi Pro League side will pay more than 21 million euros for the midfielder, whose contract with the Dutch outfit was valid until June 2027, Ajax said.
The Netherlands international joined Ajax from Tottenham Hotspur in July 2022 for 31.25 million euros, becoming the most expensive transfer in Eredivisie history.
"Steven and Ajax have made no secret of the fact that, if a good offer came from abroad, he would make the move," Ajax technical director Alex Kroes told the club website.
"That has now happened at the last minute, giving the club the necessary financial flexibility to hopefully bring in a suitable replacement in the short term."
Bergwijn won the Dutch top flight three times with PSV Eindhoven between 2015 and 2018.
He represented the Netherlands 35 times scoring eight goals, having made his debut in October 2018 in a 3-0 win over Germany in Nations League.
