The Blues confirmed the deal on their official website on Wednesday, having verbally agreed the transfer, according to the Brazilian club's president, Giovanni Luigi, earlier in the week.
No details have been released regarding the player's transfer fee or contract, but reports had claimed that the playmaker would cost around £25 million.
Oscar is currently representing Brazil at the Olympic Games and played in the Selecao's pre-tournament warm-up friendly against Great Britain.
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Goal.com exclusively revealed earlier in July that Roberto Di Matteo's club had outbid Premier League rivals Tottenham, who were also keen on the 20-year-old.
Oscar joined Internacional from Sao Paulo in 2010 and has won the Campeonato Gaucho state championship twice with the Porto Alegre-based side.
He scored 13 goals in 44 matches in all competitions last season and has found the net six times in 20 appearances during the current campaign.