The Brazilian has signed a three-year deal worth around £100,000-a-week to become Mikel Arteta's first summer signing.
The 32-year-old's preference was to remain at Stamford Bridge, but long negotiations over a new contract broke down as Willian was looking for a three-year commitment and Chelsea were only willing to offer two.
Arsenal were happy to meet Willian's demands and the winger confirmed on Sunday in an open letter to fans that his seven years as a Blue had come to an end.
It is hoped Willian's arrival will tempt club captain Pierre-Emerick Aubameyang to agree a contract extension as Arteta's vision for the Gunners takes shape.
Arteta is understood to be targeting a new centre-back and midfielder, with Lille's Gabriel Magalhaes and Atletico Madrid's Thomas Partey among their targets.
Lucas Torreira and Ainsley Maitland-Niles have interest in them and could be allowed to leave.
