The 23-year-old has signed a four-year contract with the Blues and the two clubs have agreed on a transfer fee of around £16.3million.
“Every player in the world would love to play for Chelsea and it’s a great opportunity that was given to me,” he told the club’s official website.
“I will give my best to repay this chance, and I am very happy.”
Chelsea manager Carlo Ancelotti said: “He is a fantastic player, a fantastic midfielder, he is very young and will be the future of the Brazilian national team, and I hope he will be the future of Chelsea.”