The 28-year-old becomes Jose Mourinho’s fourth capture of the summer transfer window after Chelsea clinched the signings of Cesc Fabregas from Barcelona, Mario Pasalic from Hajduk Split and Luis’ former team-mate Diego Costa.
A fee understood to be in the region of £15m was agreed between the two clubs earlier this week and the deal has now been rubber-stamped after all the formalities were completed.
Luis told the club’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 am looking forward to getting started and giving my best for the team during the coming season.”
Luis will give Mourinho extra options at left-back following the departure of the experienced Ashley Cole, who was allowed to leave when his contract expired at the end of last season and has now signed for Roma.
Cesar Azpilicueta was preferred to Cole at left-back for much of last season but is a right-back by trade and Luis’ arrival may allow him to switch back to his favoured side.
Luis was a key player for Atletico during their incredible 2013/14 campaign, when they won the La Liga title for the first time since 1996 and lost to local rivals Real in the Champions League final.
The former Deportivo man made 44 appearances over the course of the campaign and many experts felt he should have been selected for the Brazil World Cup squad but he was only named as a stand-by.