"The 25-year-old arrives on a three-year contract after passing a medical," City said in a statement on their official website.
Meteb will be officially available to play for City once he acquires work permit.
Meteb, who came through Ahli's youth ranks, proved to be a key player for the Cairo giants during the past few years.
He formed a decent attacking partnership with Angolan frontman Flavio Amado.
Meteb scored 89 goals in 172 appearances for the five-time African champions.
He was Ahli's top scorer when they won the Egyptian League title in the 2004/2005 season, notching 15 goals.
Meteb also played a pivotal role in helping Ahli claim back-to-back Champions League titles in 2005 and 2006.
On the international level, Meteb won with Egypt two successive Nations Cup titles – in 2006 and 2008.
He was Hassan Shehata's preferable option upfront during the two tournaments. He played alongside Mido in 2006 before partnering Amr Zaki two years later.
Ahli have signed Ghazl Mahalla's Ahmed Hassan and Baladeya's Hani Al-Egeizi to compensate for the departure of Meteb.