The German attacker signed for the 2.Bundesliga club over the weekend.
Frauendorf spent four years at Liverpool and posted: "As I am entering a new chapter in my career at Hannover 96 Football Club, today is the day to say goodbye and THANK YOU for the four wonderful years I spent at the Liverpool Academy.
"I could not have wished for better training conditions, and my special thank you goes out to my coaches, and to all my teammates.
"Thank you to all the staff, especially the kitchen staff, for absolutely delicious food, and thank you to my teachers who helped me succeed in the language classes.
"To all the fans who made it special to represent the Club at the matches: Thank you! The hardest part of leaving Liverpool was having to say goodbye to my host family, you certainly are more family than host parents to me, and I will miss the life with you and all the kids in the house.
"There is no way to thank you enough for everything you did for me. All the best to everyone."