The 18-year-old will not officially join Chelsea until the January transfer window but he will then be immediately loaned back to the Brazilian club until the end of the season.
Chelsea did not reveal how much they had paid to sign the player, but reports in the British media said he was valued at around £5 million ($8 million, 6.1 million euros).
The European champions reportedly acquired a 40 percent stake in Wallace as part of the deal that took Brazil-born Portugal midfielder Deco from Chelsea to Fluminense two years ago.
Wallace, a Brazil Under-20 international, will become the fifth Brazilian member of Chelsea’s first-team squad, alongside David Luiz, Ramires, Oscar and Luis Piazon.
He made his senior debut earlier this year aged 17 and went on to make 18 league appearances for Fluminense, who won the Brazilian league championship, the Rio State league and the Guanabara Cup.
Wallace’s transfer is a timely piece of good news for Chelsea, who are 10 points off the pace in the Premier League after a run of seven games without a win and on the brink of elimination from the Champions League.