The Istanbul outfit sacked Prandelli on Friday, the former Italy boss paying the price for inconsistent performances that have seen Gala eliminated from European competition.
Gala sit bottom of UEFA Champions League Group D following a 2-0 defeat to Anderlecht last week that ended any hope of a place in the Europa League.
Despite losing three league games this term, Gala are well placed to compete for a 20th Super Lig title and will hope that Hamzaoglu can inspire them to that achievement.
"I am in a place that I can call 'my home'," he told the club's official website.
"I am very happy to be here again. I'm proud of to have this important mission.
"Thanks to everyone who wanted me to come to this club. We will fight to win for every game.
"We want to achieve the goals step by step.
"Also I want to thank [Turkey coach] Fatih Terim and [Turkish Football Federation president] Yildirim Demiroren. They supported me for this position."
The 44-year-old won two Super Lig crowns as a player with Gala and has already enjoyed success in his managerial career, guiding Akhisar Belediyespor to promotion to the top flight in 2012.
Hamzaoglu's first game in charge comes against Akhisar – who he left in June - when they visit the Turk Telecom Arena on Saturday.