The Brazil international made a surprise switch to the Blues from PSG on transfer deadline day after two years away from West London.
Luiz is now hoping to get his hands on the English top-flight crown for the first time, having already won the Champions League, Europa League and FA Cup during his first stint with the club.
"I missed Chelsea a lot. I was very happy here before," he told Chelsea's official magazine. "I was also very happy in Paris. I was winning trophies, I was having a great life there but I know me and I like to have new challenges in my life, to have ambition.
"One of the reasons I decided to come back here is because I know the Premier League well but I never had the opportunity to win it, so it is still one of my goals in my career."
Luiz has started five games for Chelsea since returning, four of which have come in the Premier League.