The Brazilian has signed a three-year deal at Stamford Bridge and will wear the No.5 shirt, becoming the third member of last season's Atletico Madrid side to move to west London
Luis will wear the No.5 shirt and will fill the void left by Ashley Cole, who departed Stamford Bridge after eight years on a free transfer this summer to join Roma.
"This move is a dream come true for me. I now have the opportunity to play for Chelsea, and also in the Premier League," said the 28-year-old left-back.
"I’m very happy and looking forward to getting started and giving my best for the team during the coming seasons."
The Brazilian won four trophies in as many seasons at Atletico Madrid and played a key role in last season's remarkable La Liga triumph and Champions League run, though he could not earn a place in Luiz Felipe Scolari's World Cup squad.
Luis becomes the third member of that Atletico side to move to Stamford Bridge this summer, after Diego Costa completed a £35m move earlier this month and Thibaut Courtois returned from a two-year loan spell.