The European champions have not disclosed the terms of the transfer, but revealed the Brazil under-20 international, who has played alongside Chelsea youngster Lucas Piazon at youth international level, will remain with Fluminense until the end of the season before joining Chelsea next year.
The Blues describe the defender as an attacking right-back, and the youth international is expected to challenge Cesar Azpilicueta for the fullback berth in the long-term. A statement on the Chelsea club website said: "Chelsea Football Club is delighted to announce we have agreed terms with Fluminense for the transfer of Wallace in the January window.
"As part of the deal, the 18-year-old defender will remain with Fluminense until the end of the season."
The teenage defender made his first-team debut for his Brazilian employers at the age of 17, and Wallace has since gone on to make 18 league appearances for Fluminense.
He was part of a hugely successful Fluminense team that won the Brazilian league championship, the Rio state league and the Guanabara Cup.
The youngster was also part of the Brazil youth squad that won the South American under-17 championship last year, and the team that managed a fourth-placed finish at the under-17 World Cup.
The Blues have a growing Brazilian contingent at Stamford Bridge. Piazon, David Luiz, Ramires and Oscar form a strong Portuguese-speaking group that will welcome Wallace to Stamford Bridge next season.
Never seen the teenager play before? Watch him in action here...
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