Filipe was an integral member of an Atletico team that won the Liga title for the first time since 1996 under the stewardship of Diego Simeone last season.
He also played in the UEFA Champions League final, in which Atletico was defeated 4-1 by city rival Real Madrid after extra time.WORLD CUP: Beautiful people | Germany homecoming
The Brazilian told Chelsea's official website: "This move is a dream come true for me. I now have the opportunity to play for Chelsea, and also in the Premier League. I'm very happy and looking forward to getting started and giving my best for the team during the coming seasons."
Jose Mourinho made a new left back one of his top priorities of the transfer window.
Cesar Azpilicueta occupied the spot for the majority of the last campaign but could now revert to a more familiar right back role, while Ashley Cole ended his eight-year association with the club to join Serie A outfit Roma after his contract expired.
Filipe becomes the second Atleti player to make the switch to Stamford Bridge after striker Diego Costa too joined the Premier League outfit.
Mourinho has also added midfielder Cesc Fabregas to his ranks during the window, as he looks to build a squad that can improve on a third-place finish last season.
Filipe made 180 appearances for Atleti, winning the UEFA Europa League, Copa del Rey and two UEFA Super Cups in addition to last season's La Liga crown in his time at the Vicente Calderon.