Three Court of Appeal judges said they were left in no "lurking doubt" about the safety of Mark Litchfield's conviction.
Litchfield, 56, who had been on bail pending appeal, was led away to serve the 18-month jail sentence imposed on him at Exeter Crown Court in August.
The rejection of his appeal was welcomed by relatives and friends of 22 people who have died on ships owned by Litchfield - three on the Maria Asumpta and 19 on the square rigger Marques, which sank off Bermuda 11 years earlier.
"It is heart's ease to see justice being done," said Shirley Cooklin, who lost her 18-year-old son Ben Bryant on the Marques.
After the judgment, Suzie Macfarlane, who lost her 19-year-old daughter Emily on the Maria Asumpta, said: "I'm extremely glad it's all over - the saga has ended."
Ms Cooklin said: "It's been a tremendous strain to sit through and then to have to wait for the judgment. But I've waited 13 years for some sort of retribution. Twenty-two people have died. My fear was there would be further deaths."
Lord Justice Simon Brown, Mr Justice Rougier and Mr Justice Astill dismissed argument by Litchfield's lawyers that allegations that he was grossly negligent and in breach of his duty of care towards his crew were not supported by the evidence and should never have gone before the jury.
The Crown had alleged that Litchfield set a dangerous course before the 137-year-old vessel was driven towards treacherous rocks off Padstow, forcing him to rely on his engines which he knew to be fuelled by contaminated diesel.
The engines failed and Litchfield could not steer out of trouble. His ship broke up on rocks at Rumps Point.
Eleven survivors were rescued, but three people perished - ship's cook Anne Taylor, 50, from Wallingford, Oxfordshire; assistant bosun Emily Macfarlane, 19, of Felixstowe, Suffolk; and John Shannon, 24, the second engineer, from Queensland, Australia.
The sinking in 1984 of the Marques did not result in criminal proceedings.Reuse content