Eintracht Frankfurt receive an initial £15.4m for the 22-year-old, rising by a further £1.7m in add-ons, while Amenda has put pen to paper on a four-year contract at the CBS Arena.
Manager Frank Lampard and Coventry City's recruitment team are understood to have played a key role in winning the defender over, landing him as the club's third summer addition following the arrivals of Frank Onyeka and Loum Tchaouna.
Amenda joined Frankfurt from Young Boys ahead of the 2024/25 season, having previously won a league and cup double in his native Switzerland, and went on to make 42 appearances for the Bundesliga club. He has seven senior caps for the Swiss national team, who exited this summer's World Cup at the quarter-final stage, though Amenda was an unused squad member throughout the tournament.
On his move to Coventry City in the Premier League, Amenda said: "I'm really happy and it's a privilege to be here.
"After the first call with the gaffer, I felt the trust and I liked the project, so I feel this is a really good step for me.
"I cannot wait to meet everyone at the Club, especially the fans but of course my teammates.
"I like to defend my goal but I like to play, I'm really calm with the ball so I can help the team with this.
"I want to win, I want to help the team and help the Club succeed.
"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."
At 6ft 6in, Amenda still had three years left on his Frankfurt deal, but Coventry moved swiftly once Lampard identified him as an upgrade on the club's existing centre-back options following promotion. The fee eclipses the £7.7m Coventry paid for striker Haji Wright in August 2023, previously the club's record outlay, and signals the scale of ambition behind the Sky Blues' preparations for their first Premier League season in years.