By FOX Sports staff
The talented Brazilian had earlier been courted by Tottenham and Chelsea along with a host of other clubs in Europe.
Shakhtar, however, were unwilling to sanction a sale and refused to budge on the asking price of £34 million, equivalent to the player's release fee clause.
On the final day of the January transfer window, Shakhtar were said to have rejected a £30 million bid from the Russian club but eventually accepted an improved offer.
Anzhi, backed by a rich billionnaire, already have a roster of stars and were said to have been impressed by Willian's performances in the Champions League this season.
Although there has been no confirmation from the Russian Premier League side, Lucescu has all but confirmed Willian's exit.
"This is personal decision, and we must respect it," Lucescu told Sport Express.
"There is a club willing to pay the release clause in his contract, and Willian agreed to move. There is nothing I can do.
"To tell you frankly, I tried to convince him to stay because I think his decision is hasty and not thought out well enough. He is like a son to me.
"He came to Shakhtar almost as a child and leaves us as a 24-year-old man. I told him he would have achieved more with us when we said goodbye.
"Why did he not listen to me? I guess he was under huge pressure from his agent and his relatives that wanted to get everything at once."