"I'm very happy to be here again," the 29-year-old told Chelsea TV.
"It's fantastic to have this second opportunity to play for this club. I love this club so that's why I am here. Let's try to continue the nice history with a lot of joy and try to get success.
"It will be an amazing opportunity to show to the fans again how I love this club and how I love to play for this club. I cannot wait to wear the shirt and play at Stamford Bridge again."
Luiz has won the Champions League, the Europa League and the FA Cup at Chelsea and he is determined to add further silverware to his collection this time around.
"This is the past. We need to win again. I have the hunger to win. Of course I want to win the Premier League and of course I want to win all the titles again. I am here because I have ambition to play for a big club, and when you play for a big club you need to think about winning every single match."