The clubs reached an agreement in May over the transfer but it took a further three weeks for personal terms to be agreed.
"Right from the very first contact I had with Paris St Germain I was very happy," the player told the club's website.
"It's a big club with a great history. It's a new step in my life and I'm impatient to play for Paris and show what I can do."
Ex-Blues interim boss Rafa Benitez accommodated him successfully in the holding midfield role, before Jose Mourinho’s return to Stamford Bridge pushed Luiz back to the fringes.
Luiz joins an expensively-assembled squad at the Parc des Princes that includes Sweden's Zlatan Ibrahimovic and Brazilian team mate Lucas Moura.
Thiago Silva and Luiz were central defensive partners when the host nation kicked off the World Cup on Thursday with a 3-1 victory over Croatia.
- Sports & Recreation