The Anzhi director believes the midfielder is just below Cristiano Ronaldo and Lionel Messi in terms of talent, while he claimed wages were not a tipping point in the transfer
The midfielder moved to Russia in a €35 million (£30.1m) deal from Shakhtar Donetsk in January and Tkachenko, who works as an advisor to owner Suleiman Kerimov, feels the club have made a signing which could see them become one of the top sides in Europe.
"To bring him here was our goal, our dream. It is very easy from the middle of the table to become a good team. But when you are at the top it is more difficult," he told sports.ru.
"Willian had a desire to leave. We knew what would release him. He had a release clause in his contract and we understood we had to take the opportunity as it may not come around again.
"Willian is a man who is in a category of stars, which comes immediately after Cristiano [Ronaldo] and [Lionel] Messi."
Tkachenko also admitted that the club had looked at a number of players during the January transfer window, including Napoli's Edinson Cavani, but Willian was the only one who was affordable and was willing to leave his current club.
"We looked at James Rodriguez of Porto. He is young, but he cost €45m (£38.7m). We bid for Cavani, but his price is still €70m (£60.2m)," he continued.
"There was [Juan] Mata. There was [David] Silva. There was Oscar. There was [Javier] Pastore. There was Lucas Moura, who moved to PSG this winter. But all had no motivation to leave their current club, or the transfer fee was higher than that of Willian.
"One of the main aims for Anzhi this winter was to bring in a top attacker. The player who can bring the team to the next level."
Tkachenko moved to refute claims that the Brazil international had only joined the big-spending Russian outfit for money, and says the club were the only side to match Shakhtar's asking price.
He added: "Willian's desire to get away from Donetsk was paramount to his move. Certainly not the money. He's on the same money he could earn in Donetsk.
"We understand that you have to pay a premium, which other clubs could not afford. Tottenham offered €30m (£25.8m) and Chelsea were persistent in only offering €25m (£21.5m)."