The Blues reached an agreement to sign the left-back from the Spanish champions on Wednesday and have now agreed terms on a three-year deal.
"Chelsea Football club is delighted to announce the signing of Filipe Luis from Atletico Madrid," read a statement on the club's official website. "The Brazilian defender has signed a three-year contract and will wear the number five shirt."
The 28-year-old played an integral part for Atleti last season as they won the Primera Division and made it to the Champions League final but the Brazilian is clearly excited by the prospect of playing in England.
"This move is a dream come true for me," he said. "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."
Filipe Luis now has an opportunity to replace Ashley Cole as Chelsea's first-choice left-back in the long-term.
After missing much of the 2013-14 season through injury, veteran England defender Cole left the Blues on a free transfer in June and has since joined Roma.
Natural right-back Cesar Azpilicueta proved an able deputy to Cole and kept hold of his spot when the 33-year-old returned to fitness as Chelsea finished third in the Premier League, but Filipe Luis' arrival will allow the Spaniard to return to his preferred flank.
Filipe Luis joined Atleti from Deportiva La Coruna in 2010 and has made 98 appearances in all competitions for the Madrid side, winning the Europa League in 2012 and the Copa del Rey in 2013 before becoming a league champion.
He has four Brazil caps and was placed on the standby list for the 2014 World Cup in his homeland.