Alan Shadrake, author of "Once A Jolly Hangman: Singapore Justice in the Dock", said he could not afford to pay a Sg$20,000 (B491,000) fine on top of the prison term, resulting in another two weeks in jail.
The freelance journalist, who has worked in Britain, the United States and Asia, laughed and joked with reporters after the Court of Appeal, his last legal resort, upheld the sentence imposed by a High Court judge in November.
"I expected the decision. I am very sorry for Singapore. I'm not sorry for myself," he said after emerging from a packed courtroom.
Shadrake was granted a request to start his jail term on Wednesday after he undergoes a medical test.
He told reporters he had been receiving treatment for polyps in his colon and doctors recently found a tumour on his face.
Even if Shadrake has to serve an extra two weeks in jail for not paying the fine, Singapore prison terms are often reduced by a third for good behaviour.
The author had been on bail while seeking to reverse his conviction for "scandalising" the judiciary of the former British colony, which imposes a mandatory death penalty for drug trafficking and murder.
"We affirm the sentence imposed by the judge," Justice Andrew Phang of the Court of Appeal said Friday.
"This was still the worst case of scandalising contempt that had hitherto come before the Singapore courts," he added.
The British High Commission (embassy) in Singapore did not comment on the ruling but indirectly criticised Singapore's policies on freedom of expression.
"The British government attaches importance to freedom of expression around the world and we will continue to call on all countries, including Singapore, to recognise the right to freedom of expression as set out in the Universal Declaration of Human Rights," it said in a statement.
Shadrake's jail term was the stiffest sentence ever imposed in Singapore for contempt and was denounced by international human rights groups campaigning for an end to executions and urging greater freedom of expression in the country.
Phil Robertson, deputy director for Asia of campaign group Human Rights Watch, said the final decision was "a devastating blow to free speech in Singapore".
"It is shameful. More broadly, until the government releases its iron grip on basic freedoms, the Singaporean people will remain all the poorer for it," he told AFP from Bangkok.
Shadrake said last week that the second edition of his book was already on sale in Australia and was due to be launched in Britain on June 1.
His book includes a profile of Darshan Singh, the former chief executioner at Singapore's Changi Prison who, according to the author, hanged around 1,000 men and women including foreigners from 1959 until he retired in 2006.
Shadrake's book features interviews with human rights activists, lawyers and former police officers, and alleges that some cases involving foreigners may have been influenced by diplomatic and trade considerations.
He was arrested by Singapore police in July while visiting the city to launch the first edition of his book, which was first published in neighbouring Malaysia.
Singapore law provides that "a person commits the offence of scandalising the court if he makes statements which have an inherent tendency to interfere with the administration of justice," according to a court press statement explaining the case.
Shadrake said Friday that he might add chapters to his book detailing his experiences in prison "if it's worthwhile".