The speculation surrounding the Brazil international's future continues to gather pace with his contract at Stamford Bridge due to expire later this month.
A recent leaked clip from video game PES 21 appeared to confirm that the 31-year-old was heading for the Emirates Stadium ahead of the 2020-21 campaign.
According to ESPN, the experienced attacker has now agreed a three-year deal with the Gunners, and a move is expected to be announced before the end of August.
Willian had allegedly been keen to remain with Chelsea, but the Blues were not prepared to grant a three-year extension due to their policy on over 30s.
The South American has been in strong form for Frank Lampard's side this season, scoring 11 times and contributing nine assists in 47 appearances in all competitions.