Willian will end his seven-year spell at Chelsea this summer, the player announced on social media on Sunday.
The Brazil international had been in talks over a new contract at Stamford Bridge but negotiations broke down over the length of his deal.
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Sources have told ESPN that the 32-year-old has agreed a three-year deal at Arsenal worth around £100,000-a-week.
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"They were seven wonderful years," he wrote on Twitter. "In August 2013 when I received the offer from Chelsea, I was convinced that this was where I had to play.
"Today I am certain that it was the best of decisions. There were so many happy times, some sad, there were trophies and it was always very intense.
"Yet, beyond the trophies, I learnt a lot about myself. I developed a great deal, becoming a better player and a better person. With each training session, with each game, with every minute spent in the dressing room, I was always learning.
"I am really grateful to the Chelsea fans for the affectionate way they welcomed me at Stamford Bridge and their support throughout my time at the club.
"There was also criticism, which is normal, what is important though is that both the affection and criticism drove me to always give my all in every training session, every game, to be constantly improving until my very last minute in a Chelsea shirt!
"The time has now come to move on. I am certainly going to miss my teammates. I will miss all the staff at the club who've always treated me like a son and I will miss the fans. I leave with my head held high, safe in the knowledge that I won things here and always did my best in a Chelsea shirt!
"My heartfelt thanks go out to all of you and God bless you!"
Willian won two Premier League titles, the Europa League, the FA Cup and the League Cup during his time at Chelsea.
Source: espn.co.uk