Willian, 32, ended his seven-year spell at Stamford Bridge and signed a three-year deal with the Gunners.
Earlier this month, sources told ESPN that Willian agreed a contract around £100,000-a-week after negotiations with Chelsea broke down.
"I believe he's a player that can really make a difference for us," Arsenal boss Mikel Arteta said. "We have been monitoring him for the past few months, we had a clear intention to strengthen in the attacking midfielder and the winger positions, [and] he is a player that gives us a lot of versatility, he can play in three or four different positions.
"He has the experience of everything in the football world but to still have the ambition to come here and contribute to bring the club where it belongs. I have been really impressed with all the talks I have had with him and how much he wanted to come."
Arsenal's FA Cup final victory over Chelsea -- which Willian missed because of an Achilles injury -- means they can at least offer Europa League football next season.
Willian won two Premier League titles, the Europa League, the FA Cup and the League Cup during his time at Chelsea.
Arteta's attempts to bolster his squad this summer come amid fierce criticism of the club following their announcement that 55 members of staff will be made redundant.