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He reunites with Celtic manager Ange Postecoglou, who was previously in charge of the Socceroos.
Centre-back Jenz, 23, joins from French top-flight side Lorient on a season-long loan deal with the option to buy.
"I obviously know Aaron from my time coaching the Australian national team, and he brings with him a wealth of experience at both club and international level," Postecoglou said.
"Moritz is a player we've been aware for a while now, and I'm pleased that we've been able to sign him.
"They've already had the chance to meet the rest of the squad and I'm sure they'll settle in quickly into what is a welcoming group of players... I know our supporters will be looking forward to seeing them both in a Celtic jersey."
Celtic won the Scottish Premiership last season for their 52nd top flight league crown.