The 16-year-old will team up with the Blues after playing just 13 games for Exeter.
Exeter are now in negotiations with Chelsea over a compensation fee.
Exeter City manager Paul Tisdale, said: “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."