The clubs reached an agreement on the transfer of the Brazil forward for a reported 90 million euros ($98 million), a record for a league that is now financially backed by the oil-rich state.
Mane would be another major signing for the club that pulled off the first coup of a raft of signings by Saudi clubs, luring Cristiano Ronaldo, the five-time Ballon d'Or winner.
The former Real Madrid and Manchester United star's record-extending 123rd international goal was initially ruled out for offside before being awarded by VAR.
"The system of buying the players that almost ended their career is not the system that develops football," he said.
In the coming years, Saudi Arabia will organise the men's Asian Cup football, the Olympic-style Asian Games and even the Asian Winter Games in 2029.
In the 38-year-old Ronaldo's absence, Anderson Talisca took centre stage to score twice. He also assisted Mohammed Marwan for a third.