The Brazilian completed an £8million move to Arsenal on Thursday after he shocked the Blues with his desire to join the Gunners.
Luiz did not train on Thursday after intimating his intention to join Arsenal and some reports claimed the centre-back had fallen out with Lampard.
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He has 56 international appearances for Brazil to his name.
Unai Emery said: “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.”
David will wear the number 23 shirt.
The transfer is subject to the completion of regulatory processes.
David Luiz started his career with Vitoria in Brazil, before moving to Portugal where he played for Benfica. He also had two spells with Chelsea and spent two years in France with Paris Saint-Germain, where he played under Unai Emery.