The Istanbul team beat the visiting French team in the second and last game of the finals.
Head coach Ergin Ataman said: "I am proud of my team, the players, the fans, Galatasaray, and Turkish basketball."
Galatasaray Odeabank have now earned the right to play in the 2016-17 Turkish Airlines Euroleague.
Last week in Strasbourg, the French team had downed Galatasaray 66-62 in the first set of the two final matches.
Anadolu Agency