Luiz, a Premier League winner as recently as 2016/17 when he played 33 times en-route to glory, was an £8m transfer deadline capture for Arsenal after emerging as a shock late target.
"The cycle finished [at Chelsea]. It was a conversation between me and Chelsea and everybody. I had an opportunity to come to another big club," Luiz told Arsenal.com.
"In my life, I've always liked 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."
A report from the Evening Standard suggests that Luiz, who is believed to have pushed for the move to Arsenal, was concerned over a potential lack of playing time at Chelsea this season under the new direction of boss Frank Lampard.
The 32-year-old Brazilian had been left on the bench for last weekend's friendly against Borussia Monchengladbach, with Lampard favouring Andreas Christensen and Kurt Zouma.
Chelsea may well be concerned that Luiz's sudden exit leaves the club with minimal centre-back depth at the start of what already promised to be a difficult season after a transfer ban prevented the signing of new players during the summer.
Christensen, Zouma and Antonio Rudiger, who is returning from a knee injury, are the only three recognised centre-backs in the first-team squad, although club captain Cesar Azpilicueta has also been known to occupy the role despite reverting back to a more natural full-back position.
As far as looking forward to life at Arsenal, Luiz is hoping to win trophies with his new club, with coach Unai Emery a 'big, big part' of his decision to join and
"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," he said.
"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."