The La Liga holders had made a 25.5 million euro bid for the Brazilian, with the Blues demanding double, but the center back did not want to leave Stamford Bridge.
The Catalan giants made an initial 25.5 million euro offer to Jose Mourinho's side but were told it would take closer to 50 million euros for the Blues to sanction a sale.
"There was an official offer [from Barcelona] but I decided to stay at Chelsea," Luiz told reporters while away on international duty. "I am happy to play for a big club and be in the national team to represent my country."
Barca turned its attentions to Liverpool center back Daniel Agger after negotiations with Chelsea, but was shot down on that front as well. Coach Gerardo Martino eventually declared himself "happy with the team I have" and no defender made the move to Camp Nou.