Silva announced his farewell on Monday in an emotional video message on Chelsea's website
He was 72 and died of after a heart attack at his home in Rio de Janeiro.
A statement on Carlos Alberto's Facebook page confirmed the death.
"It is in deep sorrow that we inform that this Tuesday morning our eternal captain Carlos Alberto Torres passed away in Rio de Janeiro," the statement said.
Brazil's football confederation CBF said that the funeral would be held at its headquarters in Rio. In a statement, the CBF said "Carlos Alberto Torres leaves an enormous legacy of achievements and lots of hard work to support our football."
One of the best defenders of his generation, Carlos Alberto was innovative in playing box-to-box soccer. That style of play allowed him to score his famous goal at the 1970 World Cup, blasting in a pass from Pele in the 4-1 win against Italy in the final.
That goal, scored after a touch by almost every Brazilian on the pitch , is seen as the pinnacle of a team that was so dominant that it made their yellow shirts into a global brand.
At the end of that 1970 final, the 25-year-old Carlos Alberto became the last captain to lift the Jules Rimet trophy - the first three-time World Cup winners earned the right to keep it. The trophy was later destroyed by thieves.
After those glorious days in Mexico, Brazil won two more World Cups in much less impressive fashion. This made Carlos Alberto one of the biggest advocates among his countrymen of a return to an attacking style of football.
For many Brazilians, he was just "The Captain" - even to his friends and family. He made 53 appearances for Brazil.
"He was more than a leader, he was an innovative player. That is why he is our eternal captain," said Carlos Alberto Parreira, a physical therapist on that 1970 team and later the coach when Brazil won the 1994 World Cup.
Former Germany captain Franz Beckenbauer, writing on social media, called Carlos Alberto one of his closest friends, saying he "was like a brother to me."
Carlos Alberto's club career in Brazil was primarily with Santos, but he later played in the United States for the New York Cosmos. His friendship with Pele was built around their years at Santos. He also played for Rio de Janeiro clubs Fluminense, Botafogo and Flamengo. He retired in 1982. All of those clubs expressed condolences to his family and fans.
His coaching career was not as impressive, but Carlos Alberto still won a Brazilian championship with Flamengo in 1983. The former footballer also had a brief appearance as a city councilor in Rio from 1989 to 1993.
Carlos Alberto was working as a soccer commentator for sports channel SporTV and was on the air on Sunday covering a match.
Last month his twin brother Carlos Roberto also died.
Silva announced his farewell on Monday in an emotional video message on Chelsea's website
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