Luiz finally completed his protracted £25 million transfer from Benfica just before the window closed on deadline day on Monday.
The same night saw Torres seal a record-breaking £50 million move from Anfield as Chelsea embarked upon the biggest single-day shopping spree in their history.
While the Torres transfer was wrapped up in a matter of days, Luiz had to wait more than a month to learn his fate as the Premier League champions engaged in tortuous on-off negotiations with Benfica, which looked to have broken down completely on Friday afternoon.
But they were eventually resurrected, allowing Luiz to begin planning for his future career in London. Aware he was being pursued by Chelsea for some time, the Brazil defender had no idea Torres would ultimately join him at Stamford Bridge.
He was therefore relieved he would no longer have to face the Spain striker, who gave him a torrid time in Liverpool's 4-1 Europa League thrashing of Benfica in April.
"He is difficult of course because he is a big player,'' Luiz told Chelsea's official website. "So now I am so happy that I can play in the same team as him and not against him.''
Like Torres, Luiz sat out Chelsea's 4-2 win at Sunderland on Tuesday night, having only arrived in London that morning. But he has told manager Carlo Ancelotti he is ready to be thrown in at the deep end in Sunday's mouthwatering clash with Liverpool.
"I hope I can play quickly, and I feel 100% to play tomorrow if I need to,'' Luiz said. "I want to help the team in whichever way Mr Ancelotti wants me to do, wherever in the team. As long as I am on the field, I am happy. I am most comfortable in the centre but can play on the side also.''
Indeed, although nominally a centre-half, Luiz is comfortable across the back four. He was arguably more desperately needed by Chelsea than Torres, whose signing completely overshadowed his own arrival.
The champions have been badly short of defensive cover since Ricardo Carvalho left and Alex got injured, but Luiz is not expecting to walk into the starting XI.
"I always knew there would be competition because Chelsea is a big club and you have to be a top player to play here,'' he said. It is a big challenge for me, but I have a strong desire to get a space in this group and establish myself and learn from my new team-mates to become a better player and have more skills.
"The best league in the world is the Premier League, so I am so happy to be here playing with and against big players. All great players want to play against other great players, and I hope this is my time.''
It was not all new faces for Luiz as he met up with his team-mates at Chelsea's Cobham base on Wednesday. He knows fellow Brazil internationals Alex and Ramires well, especially the latter, who spent last season at Benfica.
"I talked with him a lot of times before my transfer and Ramires always said he hoped I would come here because it is a special place and he would be happy if I came here,'' Luiz said.
"I have known Alex for a long time. I have a lot of admiration for him, I like his football and his personality, and obviously we have both played in the national team, so he is somebody who I know well.''