The Brazilian will become Mikel Arteta's first signing of the summer when he arrives at the Emirates on what Standard Sport understands is a three-year deal.
The 32-year-old confirmed in an open letter to fans published on social media on Sunday that his seven-year stay at Chelsea had come to an end.
After initially signing a short-term contract extension at Stamford Bridge lasting until the end of the season, Willian showed impressive form following the Premier League restart, and Frank Lampard had been keen to tie the winger down to a new deal.
Chelsea were only willing to offer a two-year extension, however, with Willian holding out for three - a requirement Arsenal were happy to oblige.
Willian - who won five major trophies during his time at Chelsea - was a player specifically highlighted by Arteta, who will look to utilise his versatility and experience.
Perhaps more crucially, the imminent signing of Willian is one of obvious intent as Arsenal finally close in on a contract agreement with captain Pierre-Emerick Aubameyang.
Arsenal have also expressed an interest in Lille defender Gabriel Magalhaes as Arteta looks to strengthen his options throughout the team.