The former MSP won a defamation case against the now defunct News of The World in 2006.
The paper's owner, News Group, wanted that ruling "struck down" following Mr Sheridan's 2010 conviction for perjury.
However, the Supreme Court said they had failed to "raise an arguable point of law of general public importance".
It follows a case heard at the Court of Session in Edinburgh last year, where News Group attempted to seek permission to have the original trial rerun. That was rejected in November.
The company then appealed to the Supreme Court, which has also declined to hear the case, meaning the Edinburgh judgement stands.
In a statement, the court said: "The Court ordered that permission to appeal be refused because the application does not raise an arguable point of law of general public importance, which ought to be considered at this time, bearing in mind that the case has already been the subject of judicial decision and reviewed on appeal".
The judgement finally brings to an end an 11-year legal process, which began when the newspaper published articles about Mr Sheridan's private life.
Mr Sheridan, a former leader of the Scottish Socialist Party and Glasgow MSP, was awarded compensation after winning the defamation trial in 2006.
It is understood that Mr Sheridan was not paid the money at the time of the original defamation judgement.
In 2010, he was found guilty of perjury while giving evidence during the earlier case and jailed for three years.
He was freed from prison after serving just over a year of his sentence.
The Supreme Court has refused to hear an appeal from a newspaper group trying to overturn the verdict that saw Tommy Sheridan awarded Â£200,000 in damages.