Sheridan applied to the Scottish Criminal Cases Review Commission (SCCRC) for a review of his conviction on June 10 2014.
The Commission has now agreed to carry out the review and the case has been allocated to a senior legal officer for investigation.
Once the investigation, which is expected to take months to complete, is concluded the Commission will decide whether to refer the case to the High Court for a full appeal hearing.
Sheridan said: "It has taken a frustratingly long time to progress but at last the SCCRC has the files and my appeal against conviction has been assessed and considered worthy of more detailed analysis.
"I am absolutely confident my unsafe conviction will eventually be quashed and my name will be cleared.
"The powerful and well connected liars who coordinated my stitch up will hopefully themselves soon face justice and criminal prosecutions for their efforts to ruin other people's lives with lies, distortions and illegal activities.
"The criminal News of the World shamed the profession of journalism and was rightfully closed down. I will continue to fight the lies and distortions of the powerful gutter press with truth. I look forward to the SCCRC recommendation at the end of March next year."
The firebrand socialist was jailed for three years in January 2011 after being convicted of lying under oath during his successful defamation action against the News of the World in 2006.
The now defunct tabloid printed allegations about his private life, which included claims that he visited a swingers' club and cheated on his wife. He was awarded £200,000 in damages after winning his defamation case against the newspaper at the Court of Session in Edinburgh.
But he ended up on trial for perjury at the High Court in Glasgow, where he was convicted of the charge at the end of 2010.
Sheridan - who was freed from prison after serving just over a year of his three-year sentence - has always maintained his innocence.
In 2011, he was refused leave to appeal against the perjury conviction. His legal team wanted to argue that he had been denied a fair trial because of the amount of publicity generated before it got under way, but senior judges found the case was "not arguable".
In cases where there has already been an unsuccessful appeal or leave was previously refused, the only route back to appeal judges is via the SCCRC.
Gordon Dangerfield, Sheridan's solicitor, said: "I'm very pleased at the Commission's very prompt decision to review the conviction. This is obviously an important step forward in the process of having Tommy's conviction appealed and overturned.
"I consider that the evidence we have gathered in support of the appeal is utterly compelling. In my view, that evidence demonstrates very clearly that the conviction was a shocking miscarriage of justice, and I'm very much looking forward to the Commission's own independent investigation and decision."