The 32-year-old Brazil international ended his seven-year stay at Stamford Bridge last week after his deal with the Blues expired.
Arsenal have moved swiftly to secure the services of the two-time Premier League winner despite interest in his services from a number of Major League Soccer clubs.
"I decided [to join] because Arsenal is one of the biggest clubs in the world," Willian said. "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."
Willian will wear the number 12 jersey at the Emirates Stadium.
Arsenal boss Arteta, who led the Gunners to the FA Cup glory a fortnight ago, expressed his delight at securing a player of immense quality.
"I believe he's a player that can really make a difference for us," said Arteta.
"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."
