It comes after the Supreme Court refused an application for permission to appeal to the highest court in the United Kingdom.
Craig Murray, a former ambassador to Uzbekistan, was sentenced to jail in May after he was found guilty of contempt of court by three senior judges.
The blogger had posted a series of articles online around the trial of Alex Salmond in March 2020 after attending two days of proceedings.
The former SNP leader was acquitted of all 13 sexual offence charges following the trial in Edinburgh last year.
Mr Murray was prosecuted after concerns were raised his writing would identify complainants in the case, something prohibited by a court order.
The material included several blogs and tweets and were written over a period of a month, remaining up and unredacted despite concerns being raised the information could lead to the identification of the women who had made complaints against Mr Salmond.
The judge, Lady Dorrian, said the blogger was “relishing” the possible disclosure of the complainers’ identities and that he had deliberately risked jigsaw identification and labelled his actions “abhorrent”.
Speaking when announcing the judgement in May, Lady Dorrian said: "It appears from the posts and articles that he was in fact relishing the task he set himself, which was essentially to allow the identities of complainers to be discerned – which he thought was in the public interest – in a way which did not attract sanction."
She added: "These actions create a real risk that complainers may be reluctant to come forward in future cases, particularly where the case may be high profile or likely to attract significant publicity.
"The actions strike at the heart of the fair administration of justice.
"Notwithstanding the previous character of the respondent and his health issues, we do not think we can dispose of this case other than by way of a sentence of imprisonment."
In mitigation, Mr Murray’s lawyer Roddy Dunlop QC said the sentence was “harsh to the point of being disproportionate” and highlighted the blogger’s “impeccable character”.
Mr Dunlop said some had suggested the proceedings against Murray were “politically motivated”.
The QC said he did not make this submission himself, but “the fact remains these views are out there”.
In a press release, Mr Murray said he would surrender himself to police shortly, but would continue to fight the judgement by appealing to the European Court of Human Rights – a process that could take years.
He also continued to profess his innocence.
Mr Murray has two children aged 12 and five months and a protest against his imprisonment is planned.
Ellen Joelle Dalzell, co-ordinator of the Craig Murray Justice campaign group stated: “The sentence handed to Craig Murray not only sets legal precedent in terms of a custodial sentence for the charge of jigsaw identification, it represents an attack on free speech in general, and a tangible threat to the free reporting of legal trials in particular.”