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The 32-year-old becomes the 10th player after Emmanuel Petit, Ashley Cole, Nicolas Anelka, William Gallas, Petr Cech, Yossi Benayoun, Cesc Fàbregas, Lass Diarra and Olivier Giroud to represent both clubs.
The former Paris Saint-Germain centre-back inked a two-year deal with the Gunners and was linked with a move away from Stamford Bridge after he was seen training alone on Wednesday.
Luiz becomes Arsenal manager Unai Emery's fourth signing of the summer after securing deals for Nicolas Pepe, William Saliba, Gabriel Martinelli and Dani Ceballos.
Meanwhile, a sixth signing could be added to the ranks with Celtic defender Kieran Tierney reportedly set to join the London side as well.
Arsenal manager Unai Emery needs a bulkier defence following the departure of their captain Laurent Koscielny to Ligue 1 club Bordeaux.
