Despite being aged just 16, Ampadu featured 13 times for the Grecians last season and has previously undergone trials with Manchester United and Arsenal.
The Wales Under-19s international had yet to sign scholarship terms at St James Park, allowing him to speak to interested teams, and it has now been confirmed that he is on his way to Chelsea.
Exeter boss Paul Tisdale told the club's official website: "Everyone at Exeter City fully supports Ethan's decision to sign for Chelsea. He had many options available to him and has decided that Chelsea provides him with the best opportunity to develop the next step of his career. We wish him the very best of luck.
"Ethan has shown real maturity and professionalism throughout last season, balancing his school work with his training at Exeter City. At the same time, he has represented Wales at different age groups. We thank him for his contribution on the pitch and feel very proud of what he has become.
"Our academy should again be mentioned for the excellent work it does in not only nurturing talented footballers, but also well-rounded individuals. Ethan is another in a long line of home grown players to graduate through our academy into our first team. At Exeter City FC we will continue to support our youth system by encouraging and promoting our young players into competitive senior football when they are ready."
Ampadu, named Wales's Young Player of the Year for 2016, has also previously been linked with a move to Premier League club Liverpool.