The Brazilian instigated his move away from Stamford Bridge on Wednesday and the two clubs were able to agree a deal before the transfer window shut.
In signing for a reported fee of £7million on a two-year deal, he became the second Gunners arrival on Thursday following the earlier capture of Celtic defender Kieran Tierney.
Luiz's switch across London is one of the shock moves of the summer window, but he made it clear he wanted to make it happen when he did not train with Frank Lampard's team on Wednesday.
The 32-year-old spent seven years across two spells with the Blues, winning six major trophies, but it is unlikely he will now be remembered fondly by the club's supporters given the manner of his exit and his destination.
He is reunited with Unai Emery, who was his manager at Paris St Germain.
Emery told the club's official website: "David has huge experience and I look forward to working with him again. He is a well-known player and adds to our defensive strength."
Luiz adds experience to the Gunners' back line following the sale of captain Laurent Koscielny, who also forced his way out of the club to join Bordeaux.
The Gunners' left-back options are also strengthened following the arrival of Scotland international Tierney.
The 22-year-old has joined from the Scottish champions for a fee of £25million, though he must first overcome an injury before he can be involved.
Emery said: "We're delighted Kieran is joining us. He's a very talented player who will continue to improve.
"He increases our options defensively and I look forward to him joining our group."
Tierney, who has won 12 caps for Scotland, made over 150 appearances for Celtic after making his debut in 2014.
He said: "I'm delighted to be here. Obviously I'm injured now, but I'm just looking forward to getting back on the pitch, training and getting involved with the squad.
"I've been working hard in rehab and I've had good people around me as well. It's been easy for me. At Celtic I was training hard, working hard and just looking to get back fit. That was my main focus.
"It was the hardest decision in my whole life that I've had to make. I had to speak to my family and my close friends and my agent as well because it's a hard decision to leave a club that you love so much.
"People need to know that as well. I feel Arsenal is a massive club and it's a great opportunity for me as well. I'm delighted to be here."
The duo's deadline-day arrival takes Arsenal's summer arrivals to six, joining Nicolas Pepe, Dani Ceballos, William Saliba and Gabriel Martinelli at the Emirates, though Saliba has been loaned back to St Etienne.
There were outgoings as well on a busy day at the Emirates Stadium as Dominic Thompson signed for Brentford on a permanent deal while highly-rated striker Eddie Nketiah joined Leeds on a season-long loan.
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