Cengiz, who was the club's 37th president, took the role in January 2018 to serve until June 2021.
During his three-and-half-year tenure, the Galatasaray football team were crowned the Turkish top-tier Super Lig champions twice in 2018 and 2019.
Galatasaray, and their rivals Besiktas, Fenerbahce, and Trabzonspor, each offered their condolences on social media after Cengiz's passing.
Meanwhile, Galatasaray visited Yeni Malatyaspor in a Sunday Spor Toto Super Lig match as the teams observed a minute's silence for Cengiz before the kick-off.
He was 71.
