Some sceptics had claimed that the 24-year-old opted for the Russian club ahead of other reported admirers such as Chelsea and Tottenham Hotspur because of the salary that was on offer.
However, he has revealed that he could have earned any wages that he wanted with his former club Shakhtar Donetsk.
"Shakhtar offered me to stay with them at any price," he said. "I've earned quite a lot of money in Donetsk. With Shakhtar I also won a set of titles not only in Ukraine but in Europe also. I felt comfortable there. But the time for change has come.
"My conversation with Anzhi owner Suleiman Kerimov decided everything. After that I decided to join Anzhi.
"The club management are not only thinking about short-term gains, they really want to create a serious football infrastructure in Dagestan, to lift the game in the republic to a higher level."
Willian is believed to have cost Anzhi around £30m.