Goal understands the Blues having opted to sell their academy product for a fee believed to be in the region of £500,000 rather than loan him to a sixth different club in three years.
The midfielder made just 22 appearances for Chelsea after making his debut as a 17-year-old and has enjoyed spells with Swansea, Middlesbrough, Watford and Wigan during his time at Stamford Bridge.
"Josh is a versatile midfield player who can play in a holding role and as a playmaker," Brentford head coach, Marinus Dijkhuizen told the club's official website.
"He was a big talent at Chelsea and now I look forward to working with him and our coaching staff in order to take Josh on to the next level.
“Although he played at Vitesse last season, he has good experience of English football and will be able to fit into our playing style very quickly."