The Blues managed a great end of the season, securing Champions League football through the Premier League and winning the Europa League.
Despite doubts about the future of manager Maurizio Sarri, Luiz believes the club can fight for every title next term.
He told FourFourTwo: "The new contract [with Chelsea] means a lot as well.
"I'm glad to be here, so happy to be at this club. I love this club and I still have the ambition of a young player, so that's why I have this opportunity to show I have the same hunger.
"I think if we keep this mentality, take all the positive things we did this season and if we continue to improve and learn, we are going to be fighting for every title around the world.
"You think about winning every single competition because if it's not like that, you cannot play for a big club."