The Costa Concordia cruise ship capsized in January 2012 killing 32 people.
Francesco Schettino had handed himself in to the Rebibbia prison in Rome after the verdict, his lawyer said.
He was sentenced in 2015 after a court found him guilty of manslaughter, causing a maritime accident and abandoning ship.
The Costa Concordia cruise ship capsized after hitting rocks off the Tuscan island of Giglio.
Francesco Schettino was nicknamed “Captain Coward” by the media, after the coastguard released recordings of him in a lifeboat resisting orders to return to the stricken vessel.
More than 4,000 people were aboard at the time and were forced into a chaotic evacuation.
Prosecutors say Francesco Schettino steered too close to the island to show off to a dancer, Domnica Cemortan, who was with him at the helm.
However, he blamed communication problems with the Indonesian helmsman.
The court ruling was welcomed by a lawyer representing relatives of the victims, who said it represented justice at last.
The sentence included 10 years for manslaughter, five for causing the shipwreck, one for abandoning the ship before passengers and crew were clear, and one month for lying to the authorities afterwards.
Costa Crociere, the company that owned the Costa Concordia, sidestepped potential criminal charges in 2013 by agreeing to pay a €1 million ($1.1 million) fine.
Five of Francesco Schettino’s colleagues were also jailed for up to three years in earlier cases.
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