Neymar scored for Paris St-Germain in their pre-season friendly against Jeonbuk Hyundai Motors
The transfer is subject to the 31-year-old completing a medical and all necessary paperwork.
Neymar, who joined PSG for a world-record fee of £200m in 2017, was left out of their squad for the Ligue 1 draw against Lorient on Saturday.
He was not part of coach Luis Enrique's plans for the new season.
His exit also fits PSG's strategy of moving away from the 'Galacticos' era of signing high-profile players for big fees and significant wages, with Lionel Messi also leaving the club earlier this summer.
Neymar was understood to be earning in the region of 25m euros (£21.6m) annually at the French side.
He will reportedly be paid 150m euros (£129.2m) a year in Saudi Arabia - six times the amount he earned at PSG.
The Brazilian made 173 appearances for PSG, helping the club win 13 trophies, including five Ligue 1 titles, as well as reaching the 2020 Champions League final.
However, his time in the French capital has also been hampered by a number of ankle injuries.
The former Barcelona player had surgery in March that caused him to miss the rest of the season and he only resumed training in July.
He missed two of Brazil's matches at the 2022 World Cup after being injured in their opening group match.
The forward also missed the 2019 Copa America after suffering torn ligaments in his right ankle and was out for several weeks in 2021 with a similar injury.
News of the Neymar deal comes just 24 hours after PSG's Kylian Mbappe was reintegrated back into first-team training after positive talks with the club.
The France forward, 24, had been in a contract stand-off amid a desire to join Real Madrid but could now extend his contract at PSG, with his current deal due to expire next summer.
Mbappe was also left out of the squad for the Lorient game and watched the match from the stands.
Last month, PSG gave Al-Hilal permission to talk to Mbappe after the Saudi side made a world-record £259m bid.
If completed, the Neymar deal will continue a remarkable summer spending spree by Saudi clubs, underlining the league's ambition to be one of the top competitions in the world in the next few years.
The likes of Karim Benzema, N'Golo Kante, Jordan Henderson, Ruben Neves, Sadio Mane and Roberto Firmino have all moved to Saudi Arabia.
Portugal superstar Cristiano Ronaldo joined Al-Nassr from Manchester United in January.
After Riyad Mahez left Manchester City to join Al-Ahli in July, Pep Guardiola said the Saudi league's financial muscle has "changed the market".
"A few months ago when Cristiano [Ronaldo] was the only one to go, no-one thought this many top, top players would play in the Saudi league," the City manager said.
"In the future there will be more and that's why clubs need to be aware of what is happening.
"I don't know how long they will sustain it, but the feeling is that they will stay. The players want to take this experience to play in that league and they are able to do it."
-- Courtesy of BBC Sport