Fernando Torres' arrival also boosts Italian's options up front
The Blues brought in the centre-back from Benfica during the January transfer window for a fee believed to be in the region of £21.3 million.
At 23 years old, Luiz is widely seen as a long-term replacement for Terry, and the former AC Milan boss told Chelsea's official website: "With Luiz we can have more rotation with our players and maintain more fresh defenders.
"Now we have lot of opportunities to choose players, give someone else a rest and to maintain every defender's fitness for the rest of the season.
"When a good player with a lot of skills comes to improve the squad, everyone is happy. Obviously everyone knows that in the top teams there is competition to play. This is normal. It's a good motivation for everyone.
"We will not have a problem in the centre of defence in the future."
The £50m arrival of Fernando Torres has also given the Italian boss more options in attack, as he played three strikers in the form of Nicolas Anelka, Didier Drogba and Torres against Liverpool.
But there have been reports pointing towards Drogba being dropped, should the ex-Roma manager favour a formation with just two forwards.
"Now we have a strong squad with David Luiz and Torres. We've improved our ability and we have more power," said the 51-year-old.
"The squad was good, but now it is even better. In attack we can choose whether to play with two up front or with the Christmas tree, it depends on the game that we want to play.
"When we play with two strikers Nicolas Anelka can be in the No.10 position, in the hole, but with one striker he can play on the right.
"Florent Malouda can also play there, and we tried last year having Frank Lampard there at the beginning of the season which was not bad.
"Malouda can also play in the Christmas tree, but I don't need to think of him as a central midfielder because we have a lot of options there."