In Neymar transfer news, the deal for the former Barcelona player is understood to be worth about 90m euros (£77.6m) plus add-ons, the club announced.
Neymar, who joined PSG for a world-record fee of £200m in 2017, was left out of their squad for Saturday's Ligue 1 draw against Lorient.
The 31-year-old 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.
"I am here in Saudi Arabia, I am Hilali," Neymar said in a video posted to the club's social media accounts.
The forward was understood to be earning an annual income in the region of 25m euros (£21.6m) 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.
"It is always difficult to say goodbye to an amazing player like Neymar, one of the best players in the world, said Nasser Al-Khelaifi, PSG's president and chief executive.
"I will never forget the day he arrived at Paris St-Germain, and what he has contributed to our club and our project over the last six years."
Neymar's time in the French capital has also been hampered by a number of ankle injuries.
He had surgery in March that caused him to miss the rest of the season and he only resumed training in July.
In the other Neymar transfer news, the forward missed two of Brazil's matches at the 2022 World Cup after being injured in their opening group match.
He 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.