Faivre joins the Saudi Pro League side having made just six appearances for the Cherries since joining the club in July 2023.
In the time since, he has been on two loan spells at Lorient and Brest back in France, and returned from the latter club for preseason with Andoni Iraola's side.
He did feature for Iraola's Cherries across the summer's friendlies, but dropped out of the match day squads for the first three competitive games of the season.
The 27-year-old returned to the bench in the 1-0 win over Spurs before the international break and deadline day, where he was close to joining Verona.
But he opted not to sign for the Serie A club and the deal fell through, having turned down the opportunity to speak to Southampton, Leicester, Copenhagen and Birmingham.
A statement from the Cherries said: "AFC Bournemouth would like to wish Romain all the best for his loan move with Al Taawoun."