Firmino has agreed to a two-year deal with the champions of the Qatar Stars League, having guided Al-Ahli to the Asian Champions League Elite title in Jeddah this past May.
"I am pleased because we created history at the club during our two years together," the Brazilian expressed in a farewell video shared by the Saudi club.
"The highlight was becoming champions of Asia. I am truly thankful for this."
Firmino spent two seasons with Al Ahli after his transfer from Liverpool and played a pivotal role in the club's first continental title victory, netting six goals in 12 matches in the Asian Champions League Elite.
He assisted both of his club's goals in their victory against Japan's Kawasaki Frontale in the final in May, making him the first player - alongside teammates Riyad Mahrez and Edouard Mendy - to secure continental titles in both Asia and Europe.
Firmino's outstanding performances earned him the title of the competition's most valuable player.
The 33-year-old joins an Al-Sadd team that clinched last season's domestic championship to secure a spot in the upcoming edition of the Asian Champions League Elite.