The 28-year-old arrives at Stamford Bridge for a fee reported to be 20 million pounds ($34.24 million) as a replacement for Ashley Cole, who left Chelsea at the end of the season and joined Serie A side AS Roma earlier this month.
"This move is a dream come true for me," Luis told the club website (www.chelseafc.com). "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."
Luis was a key member of the Atletico team who defied the odds last season to win La Liga and fell minutes short of winning the Champions League final, before losing 4-1 in extra time against rivals Real Madrid.
He becomes Chelsea's fourth close-season signing following the arrivals of former Atletico team mate Diego Costa, Spain midfielder Cesc Fabregas from Barcelona and midfielder Mario Pasalic from Hajduk Split.
(Reporting By Tom Hayward; editing by Toby Davis)
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