The 29-year-old left Chelsea for PSG two years ago but is back at the west London club after a trophy-laden spell in France for a fee said to be in excess of 30 million pounds according to British media reports.
"I'm delighted to return to Chelsea," the defender told the club's official website (www.chelseaf.com). "We had a fantastic story during my first time at the club and I want to help the team and (manager) Antonio Conte achieve a lot of success.
"I always had a wonderful relationship with the fans and I am looking forward to wearing the blue shirt at Stamford Bridge once again."
PSG paid a reported 50 million pounds, a world record fee for a defender, when Luiz moved to Chelsea in June 2014.
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In three seasons at the club, after joining from Benfica in 2011, Luiz won the Champions League, Europa League and FA Cup but was sometimes criticised as being unreliable under pressure.
He won two consecutive Ligue 1 titles in France and has played more than 50 times for Brazil since his first cap in 2010 although he was left out of the 2016 Copa America squad.
(Reporting by Steve Tongue and Ed Dove; editing by Ken Ferris)
