The Evening Standard reports that the former Chelsea man had a medical with the north London club this morning.
The Brazilian announced his departure from Chelsea on Sunday by releasing a statement confirming his exit after seven years in west London.
The 32-year-old wanted a three-year deal to extend his stay with the Blues but that his demands were refused and was offered a two-year deal.
Willian therefore decided to leave and Arsenal were willing to give him the three-year deal he craves, albeit on slightly less than his £120,000-a-week salary at Stamford Bridge.
