The Brazilian has spoken of his joy at signing for Guus Hiddink's side, and has expressed gratitude towards his former club Shaktar Donetsk
The 24-year-old had previously been strongly linked with a move to either Chelsea or Tottenham, but he elected to join the Russian side instead.
"I'm happy to be with Anzhi!" he told his new team's website. "This is a club with serious infrastructure and big goals.
"They have a strong team managed by one of the best coaches in the world. I'm sincerely happy to become a football player for the Dagestani team."
The Brazilian international will provide yet more attacking talent in a side that already has the likes of Samuel Eto'o, Lacina Traore and Mbark Boussoufa at its disposal.
Willian also spoke affectionately of his former club Shakhtar Donetsk, but admitted that "now it's time for a new step in my life".
"I spent five and a half years in Donetsk. There were great people and great relationships within the squad. We won numerous titles and I wish success to my former team-mates."
Anzhi are currently second in the Russian league, but with no fixtures until March they will focus their attention on their Europa League clash with Hannover in February.