Brown, 16, made his debut for the midlands outfit last season, coming off the bench in the 3-2 Barclays Premier League home loss to Wigan in May - his sole senior appearance to date.
He has been capped by England at Under-16 and Under-17 level.
A statement on West Brom's official website said: "Albion have today rejected an offer from Chelsea for academy product Isaiah Brown.
"Under Premier League rules the Baggies are due compensation from the London club for the 16-year-old midfielder, who has been at the Hawthorns for three years and had agreed to sign scholarship forms."
Albion sporting and technical director Richard Garlick said: "We are disappointed by Chelsea's offer.
"We have invested a lot of time and money in Isaiah's development as a player and - as one of our most exciting academy products in recent years - we had hoped to bring him through into our first team.
"But Chelsea have forced our hands and we are more than prepared for the matter to be decided by a tribunal if needs be.
"More importantly, it makes you question why these young players are joining bigger clubs when they are likely to gain more first-team opportunities in the Barclays Premier League at clubs similar to us."