Gary Cahill served as vice-captain to Terry last season and wore the armband in most games as a result of the veteran skipper rarely playing.
For now, Luiz is expecting Cahill to retain the role, although the Brazilian will still aim to be a leader himself as one of the senior and most experienced players in the squad.
"I think it continues to be Gary, why not? But it's not about the armband, it's about your leadership every day and your discipline and the way you try to help the team," Luiz told the Daily Mail.
"I already had the armband here and I always try to be a leader and try to help. I love the responsibility. I was the youngest captain in Benfica's history, so I have always taken responsibility.
"When you play for big clubs you always have responsibility. This will just carry on."
Despite Terry's exit to Aston Villa and Kurt Zouma's impending loan to Stoke, competition for centre-back places will still be strong at Stamford Bridge this season.
Last season's premier back-three of Cahill, Luiz and Cesar Azpilicueta have been joined by £34m signing Antonio Rudiger from Roma, with one of the four set to miss out each game.
"We need to build a strong squad and a strong team. We need to do better than last season if we want to win again the Premier League and do well in Europe in the Champions League," Luiz said.
"Everybody will want to beat our team and we need to improve ourselves to be better than last season."