Sources have told ESPN that Luiz, 34, will leave the club when his contract expires at the end of the season after talks ended without an agreement over an extension.
Although Arsenal have suggested they made the decision to end his involvement with the club, sources close to Luiz have told ESPN he in fact chose to walk away.
Luiz has made a total of 73 appearances for Arsenal since joining for them for £8 million from Chelsea in 2019. He was considered an influential figure in the dressing room, having won four major trophies at Stamford Bridge, including the Premier League and Champions League.
"He is a player who has won everything in football and has earned every right to do so through who he is as a player and as a person," Arteta, who inherited Luiz as part of a squad he took charge of in December 2019 following Unai Emery's sacking, said at a news conference on Tuesday.
"I had the privilege to work with him for 18 months. I really enjoyed it. I think we got on really good. I think we had some great moments together.
"He's been really helpful, someone who we really like and appreciate so much. So I say thank you to him and wish him the best of luck in his next chapter because I'm sure, knowing David, that he will have many more to come as player and in the future somehow related to the game.
"When you get to know the person, his background, where he was raised in Brazil and what he's done. To get to this point is remarkable.
"You understand a lot of things happen for a reason and it's not just an ability, a quality or a determination. It's many other factors.
"I've really enjoyed and learnt from him. He's been very helpful every time with the team and I feel sadness as well because you get attached to the players emotionally.
"One is the player and we have to get the maximum out of him, and then it's the person. And when it gets to this stage it's tough and it hurts because that relationship now is going to be going away, at least in this space and not seeing him every day. Again, I have to say thank you to him."
Pushed on whose decision it was to part company, Arteta said: "It's after a few conversations that we had, David and I.
"We discussed this situation in different occasions, and the other day we made the final decision on that.
"We have very clear talks in the last few months. We already had a big decision to make last year when we had to extend his contract in a very difficult moment during the COVID-19 world. With the pay cuts and everything, we managed to extend that for one more season.
"He's given his best. I tried to help him as much as I possible could. The club as well. And after some conversations we decided that it was the best way to do it now."
Arteta was coy on whether William Saliba would now finally get his chance to kick-start his Arsenal career having been signed for £27m from Saint-Etienne in 2019 only to be loaned back to the Ligue 1 club for a year before spending the 2020-21 campaign at Nice.
"You will see in the summer the possible replacements; William is our player for sure, and that is a decision we are going to be taking in the summer," Arteta added.
"When we finish the season we will sit down and discuss the roles of every member of the squad and how they can fulfil that role.
"He is our player, so he will be back here for sure, and after that we will make the decision based on the agreement of the role he is going to play in the squad."