The Brazilian midfielder, who spent seven years at Stamford Bridge, was available on a free transfer after failing to agree a new deal with Chelsea.
The Blues had offered the 32-year-old a two-year contract, however, Willian and his agent, Kia Joorachbian, held firm on their demands for a three-year deal and negotiations reached an impasse.
Arsenal were willing to meet those demands, though, with head coach Mikel Arteta keen to add experienced players to his squad.
“I believe he’s a player that can really make a difference for us,” Arteta said upon confirmation of the deal.
“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; 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.”
Willian is delighted to have made the switch across London describing the Gunners as “one of the biggest clubs in the world”.
“I’m very excited to become an Arsenal player – I can’t wait to start training and playing with my team-mates,” he added.
“I decided [to join] because Arsenal is one of the biggest clubs in the world. They have a new project with Mikel Arteta.
“I think this club deserves to shine again and I want to be a part of this project – to be a part of the Arsenal family is amazing. I’m very happy to do that.
“I come to try to win trophies, because this club deserves to win again, and I think you have to do the best as possible to win every game.
“I always train hard and go on the pitch giving 100 per cent to help this team to win games and to win titles as well.”