Ramires, who helped Benfica to the Portuguese title last season, will bolster a Chelsea squad which has been stripped of experienced midfielders Deco, Michael Ballack and Joe Cole since the Blues completed the Premier League and FA Cup double.
"Every player in the world would love to play for Chelsea and it's a great opportunity that was given to me, I will give my best to repay this chance, and I am very happy," the 23-year-old, who agreed a four-year deal after passing a medical, told Chelsea's website.
The fee was in the region of 17 million pounds, British media said.
"He's a fantastic player, he's a fantastic midfielder. He's very young, he will be the future of the Brazilian national team and, I hope, he will be the future of Chelsea," Chelsea coach Carlo Ancelotti told reporters.
Rio-born Ramires made his debut for Brazil in 2009 and appeared in four of his country's five matches in South Africa but was suspended for the quarter-final defeat by the Netherlands.
Chelsea could find themselves in hot water over Neymar after his club Santos threatened to report them to FIFA for speaking to the player directly.
Ancelotti said he had not been involved in the situation.
"I don't know nothing about this. All I can say about Neymar is he's a fantastic player. He's not a Chelsea player now and it's difficult for me to speak about this.
"What happens after I'm not interested, I can say only about his technical quality. We are interested in all the young players who come through in all the world. Neymar is one of these. But this doesn't mean we have to buy this player."
NOT WORRIED
Chelsea have been unimpressive in their pre-season matches and were well beaten by Manchester United 3-1 in the Community Shield at Wembley Stadium on Sunday.
But Ancelotti said there were reasons for that and he was not unduly worried as several of his key players are returning to fitness, although midfielder Frank Lampard is a worry ahead of Saturday's opening game against West Bromwich Albion.
"(Goalkeeper Petr) Cech is ready, Alex is ready but (Jose) Bosingwa is out again. He's doing individual training. We had some problems with the international matches, not all the players are ready to play.
"We have to have a check with (Frank) Lampard because he had a problem with his ankle. We have to do a check and then we decide if he is ready or not. Petr Cech will start. We are ready to defend the title.
"We have a fantastic motivation to try and win again. We said last year with the victory in the Premier League and FA Cup we had the possibility to open a new cycle and we want to do that.
"It's in our minds to do our best. We know the other teams will work harder
