The 32-year-old spent seven years at Stamford Bridge across two trophy-laden spells, before joining Arsenal on transfer deadline day in an £8million deal.
Luiz was said to be concerned about his first team opportunities under new manager, Frank Lampard, after he was a key member of Maurizio Sarri’s team last season.
The Brazilian defender was dropped for last Saturday’s friendly against Borussia Monchengladbach and was subsequently told to train away from the first team on Wednesday.
Asked why he left Chelsea, Luiz told Arsenal’s official website:
“The cycle finished there.
“It was a conversation between me and Chelsea and everybody. I had an opportunity to come to another big club. In my life, I’ve always liked to do some challenges.
“I’m not scared at all to try things. I think not too many players would make this kind of move, they would maybe be scared, or something like that. I’m just trying to do big things in my life, so like I said, my cycle at Chelsea finished and now I’m excited to start a new chapter of my life here.
“It’s [Arsenal’s] a big club – not just in England, but everybody around the world knows how big Arsenal is.
“When I had an opportunity to come to this kind of big club, I had to take it. That’s why I’m here.”
Luiz played briefly under Unai Emery at Paris Saint-Germain and admitted the Spaniard also played a big factor in his decision to join Arsenal.
“A big, big part. I know him, I know some people from the club.
“I know Edu, I know Raul, I know the quality of the team, the players, and that’s what makes me excited to dream, to have the ambition to win big things.
“I think all my life, I’ve always started the season with the goal to win things. It’s not going to be different here – I’m going to come with this mentality because this is what made me move here.
“This is what makes me feel good every single day. I have to run for one reason, for one goal, and my goal is to win things with Arsenal.”