Chelsea announced on their website that they have agreed terms both with Anzhi and the 25-year-old himself to bring him to Stamford Bridge for a reported £32.5 million.
The former Shakhtar Donetsk star has played only twice for the Brazilian national side in the last two years, far short of the stipulation that players must have appeared in 75 per cent of their country's internationals over the past two years.
Yet Chelsea are almost certain to be successful arguing that he falls in to the 'special talent' category, given their own status within the game and the wealth of talent at Brazil's disposal.
Russian newspaper Sport Express had reported on Saturday that the move would be announced on Sunday or Monday for 38m euros, a discount on the 41m euros paid by Anzhi for the attacking midfielder in the January transfer window.
Jose Mourinho also added on Saturday that the player had "already made his decision" to join Chelsea, despite having undergone a medical with Tottenham.
Tottenham's own interest in the playmaker came only after widespread reports emerged that Liverpool had agreed personal terms with the player.
Chelsea's bid was apparently boosted by the rare direct intervention of Blues owner Roman Abramovich, who reportedly contacted Anzhi owner Suleyman Kerimov - a personal friend - to help oil the wheels of a deal.
Willian has long been linked with a move to the Premier League, with Chelsea first being linked with the Sao Paulo-born player two years ago.