The 22-year-old made 22 appearances in all competitions for the reigning Premier League champions but the last of those came in the 2011-12 season before a series of loan moves.
McEachran spent time with Swansea that season and also had loan spells with Middlesbrough, Watford, Wigan Athletic and most recently Dutch side Vitesse Arnhem.
Brentford’s new head coach Marinus Dijkhuizen said: “Josh is a versatile midfield player who can play in a holding role and as a playmaker.
“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.”
The club’s co-director of football Phil Giles added: “Josh is a player who our scouting team followed closely during the second half of last season.
“We quickly recommended him to Marinus, who of course knew Josh from his time in Dutch football and was quick to add his agreement to the discussion to proceed with the transfer.
“We are sure Josh can continue to develop and that, at 22, he still has many great seasons ahead of him. We welcome him to Brentford and to pre-season training in Portugal.”