The Brazil international had been linked with a move to Liverpool and Tottenham during the transfer window, but Chelsea appeared to sneak under the radar to secure the attacking midfielder's signature.
However, Willian has explained that a move to Stamford Bridge had been on the cards for two months prior to his move.
The 25-year-old signed for Anzhi Makhachkala in January from Shakhtar Donetsk, but the Russian club's decision to cut costs left him seeking a move.
And Willian has insisted that Chelsea were the only club he was interested in joining as a departure from Dagestan became necessary.
"They [Chelsea] made an offer two months ago but I was not allowed to leave," the playmaker told Brazilian television station Sportv.
"I kept following the club and I used to go to London to follow Chelsea whenever I had free time and now my dream has come true.
"Other clubs were interested, but my intention and dream of playing for Chelsea made the difference."
Willian made just 15 appearances for Anzhi before agreeing his move to Chelsea on August 25.