Throughout the course of last season, the 32-year-old has been locked in talks with Chelsea representatives about a potential contract extension, but it is believed the club were not willing to meet his request of a three-year deal.
Arsenal, however, have matched his personal terms and he will play under Mikel Arteta next season.
The Spaniard is delighted at being able to bolster his attacking ranks.
"I believe he's a player that can really make a difference for us," said Arteta.
"We had a clear intention to strengthen in the attacking midfielder and the winger positions.
"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 still has 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."
Willian joined from Russian side Anzhi Makhachkala for £30m seven years ago, and since then has won two Premier League titles, one FA Cup, and one Europa League.