"We pick the best, and he’s one of them," Al-Ahli posted on messaging platform X, previously known as Twitter.
Saint-Maximin, 26, will team up with former Premier League players Roberto Firmino, Edouard Mendy and Riyad Mahrez at Al-Ahli.
Saint-Maximin was left out of Newcastle's pre-season tour of the United States, with manager Eddie Howe saying the club had to sell a player during this window due to UEFA's Financial Fair Play Regulations.
The Public Investment Fund, which is the sovereign wealth fund of Saudi Arabia, owns 75% and 80% of Al-Ahli and Newcastle, respectively.
Saint-Maximin joins a growing list of high-profile names to move to the Middle East in recent months, with Ballon d'Or winner Karim Benzema, N'Golo Kante and Ruben Neves among those following in the footsteps of Cristiano Ronaldo, who moved to Al-Nassr in January.