The 22-year-old centre back arrives after two seasons with the Bundesliga side, where he made 42 appearances in all competitions. He has seven caps for Switzerland.
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"I want to win, I want to help the team and help the club succeed," Amenda said in a statement.
"I'm really looking forward to playing in this beautiful stadium, to meet the fans, to celebrate with them, to win with them. I want to score here as well so I can't wait to get started."
Coventry begin their Premier League campaign away to defending champions Arsenal on August 21st.