The 32-year-old Brazilian centre-back has signed what is believed to be a two-year deal at Emirates Stadium, helping to plug the gap left by captain Laurent Koscielny's departure to Bordeaux.
Omnisport understands the transfer is worth around $10million (£8m), bringing an end to David Luiz's second spell at Chelsea after a two-year stint at Paris Saint-Germain where he worked with Unai Emery.
David Luiz first joined Chelsea from Benfica in 2011, before departing for Paris three years later. He returned to west London in 2016 and won the Premier League title in his first season back at the club.
The defender was a regular under Maurizio Sarri last term and it appeared he would again play a key role under new boss Frank Lampard.
However, reports emerged on Wednesday that David Luiz was keen on a move to Arsenal and he could now make his debut away at Newcastle United in the Gunners' Premier League opener on Sunday.
Chelsea released Gary Cahill at the end of last season and cannot replace either their former skipper or David Luiz due to a transfer ban, although Kurt Zouma and Fikayo Tomori have returned from loan spells and Antonio Rudiger is nearing a return to fitness.