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.
"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."
Hamzaoglu's first game in charge comes against Akhisar – who he left in June - when they visit the Turk Telecom Arena on Saturday.
