The Brazil international, 27, has signed a five-year deal that makes him the most expensive defender in football history.
"Right from the very first contact I had with Paris St Germain I was very happy," he said.
"It's a big club with a great history, a new step in my life, and I'm impatient to play and show what I can do.
"I will be defending the colours of one of the biggest clubs in the world. It will be a great time for me, both professionally and personally. I want to enjoy myself and, if possible, win as much as possible."
Sky sources revealed last month that the clubs were in advanced talks over the transfer, before Luiz all but confirmed its conclusion in a public 'thanks and goodbye' to his former club.
Ahead of the World Cup, where Luiz is currently part of the Brazil squad, the centre-half said he was sad to leave Stamford Bridge and thanked Chelsea "for three-and-half-years of a great partnership".
Luiz joined Chelsea from Benfica in 2011 for an undisclosed fee thought to be around £25m - part of a deal that saw Nemanja Matic move the other way before his return to west London last summer.
Sao Paulo-born Luiz, who began his career with Brazilian side Vitoria, made 81 appearances for Chelsea in a three-year spell, scoring six goals.
He won a UEFA Champions League and FA Cup double in his first season under Roberto Di Matteo and then lifted the UEFA Europa League under Rafael Benitez in 2013.
But he was on the periphery of Jose Mourinho's team last season, and predominantly used in midfield rather than in his favoured position at centre-back.
Luiz, capped 37 times, joins his Brazil central defensive partner, Thiago Silva, at the heart of PSG's defence, as well as compatriots Maxwell, Marquinhos and Lucas Moura.