Chile Under-20 star Cuevas impressed in a trial last year and the 18-year-old has signed a contract at Stamford Bridge until 2018 after announcing he had agreed a deal in February.
He came through the youth ranks at O'Higgins before breaking into the first team and playing in the top flight in Chile.
Cuevas played in four of his nations' five games in the U20 World Cup this summer in Turkey and helped Chile to the quarter-finals before losing to Ghana.
Reports in South America had revealed Chelsea offered an initial $2.6million (£2.2m) for the teenager, but his club were rumoured to want $4m (£3.4m) before agreeing to a sale.
"I'm very happy," said Cuevas, who can play at left-back or on the left wing. "Chelsea were following me for more than a year. What I wanted happened, which was joining this club."