On Sunday, the Brazilian - whose temporary contract extension expired after Chelsea's long 2019/20 campaign finally concluded with a 4-1 Champions League defeat by Bayern Munich at the weekend - announced in an open letter to fans that the "time has come to move on".
He wrote: "They were seven wonderful years.
"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!"
Standard Sport understands that Arsenal now hope to complete the signing of Willian on a free transfer this week, with the player - who turned 32 on Sunday - set to pen a three-year contract with the Gunners having rejected Chelsea's offer of a new two-year deal.
Chelsea boss Frank Lampard previously said that there would be no hard feelings if Willian were to complete a move to Arsenal, with the Blues paying glowing tribute to the experienced winger and offering a look back at his successful career in west London via their official website on Monday.
"Away from the field of play Willian has been a supremely friendly and calm member of the squad for seven seasons, and his big grin will be missed by all at Cobham," Chelsea wrote.
"In training and in games, he combined Brazilian flair with a hard-working mentality that ensured he was highly valued by each of his Chelsea managers, and rarely out of the team for long, despite stiff competition for places.
"Capable of the extraordinary, a significant contributor to five trophy wins, and a class act on and off the pitch: when Willian saw the light in 2013, he could not have hoped for a more comprehensive vindication of his decision over the next seven years.
"He leaves Chelsea with our best wishes for the future, and with so many wonderful moments etched in our memories."
Willian famously pulled out of a move from Russian side Anzhi Makhachkala to Tottenham to sign for London rivals Chelsea in 2013 and went on to score 63 goals and provide 62 assists in 339 appearances for the club across all competitions.
The former Corinthians and Shakhtar Donetsk star won two Premier League titles at Chelsea in 2014/15 and 2016/17, also lifting the FA Cup, Carabao Cup and Europa League trophy during his tenure.
Chelsea also bid a similar farewell to another departing winger in Pedro, who is leaving the Bridge after five years and 206 appearances following the end of his contract in order to join Serie A outfit AS Roma.
"It was rare for any game to pass Pedro by, and in his 206 appearances for us he scored 43 goals and provided 28 assists," Chelsea wrote.
"So many of those came at significant moments; plenty were of elite quality.
"In his first interview with this website upon signing in August 2015, Pedro said he wanted to test himself in a new league after so many successful years at Barcelona, and ‘help Chelsea win titles’.
"They were challenges he emphatically met during five years of loyal service for which everyone at Chelsea is thankful. Good luck Pedro!"