The announcement came after Mr Coulson, the former editor of the News of the World, was questioned for six-and-a-half hours in Glasgow after being detained at his home in London yesterday morning.
In a statement released at 9.50pm, Strathclyde Police said: "A 44-year-old man has been arrested in connection with alleged perjury before the High Court. A report will be submitted to the procurator-fiscal."
The journalist-turned-political strategist was visited unannounced at his home in Dulwich at 6.30am by seven Strathclyde officers before being driven under escort to Glasgow.
Extra officers were used as an operational precaution because it was not known how many people would be in the house.
At 3.20pm Mr Coulson arrived at Govan police station in Glasgow in a black people carrier. He is believed to have left by a side entrance following his arrest.
The high-security police station, used to question terror suspects, is the base for Operation Rubicon, the inquiry set up to investigate allegations of phone-hacking, breach of data protection and perjury surrounding the trial that led to Sheridan receiving a three-year prison sentence.
The 48-year-old former Scottish Socialist Party leader vowed to clear his name after he was released from Castle Huntly prison near Dundee on January 30, after serving one-third of the sentence. He is considering an appeal.
Commenting yesterday on the news that Mr Coulson had been detained, Sheridan said he believed it was the first step "in the journey towards the quashing of my conviction, which was unsafe and unsound".
Mr Coulson was serving as the Prime Minister's chief media adviser at 10 Downing Street when he was called as a defence witness by Sheridan, who was on trial for lying in court when he won a £200,000 defamation action against the News of the World in 2006.
However, current SSP leader Colin Fox last night attacked his former comrade. He said: "It is time Tommy Sheridan stopped shamelessly milking the public anger about the deplorable actions of the Murdoch press and started telling the truth that he lied in his libel case, was found guilty of perjury. Regardless of the outcome of the Coulson inquiries that remains the case."
Mr Coulson was questioned over two days at the High Court in Glasgow by Sheridan, who conducted his own defence.
In May 2010, Mr Coulson was unveiled as director of communications and planning with the Conservative Party.
He became Mr Cameron's trusted media adviser but stepped down in January 2011.
Sheridan said that the work of Strathclyde Police's Operation Rubicon, which is examining whether witnesses lied to the court during his trial as part of its investigation into phone hacking, helped his hopes of overturning his conviction.
Speaking alongside him outside his home, the former MSP's lawyer, Gordon Dangerfield, said: "We have very strong grounds of appeal and will be lodging a full appeal in due course.
"Today's developments concern only one of various areas which are relevant to the appeal, and which are being actively pursued by us.
"We are very limited in what we can say because much of the information which we have is still confidential at this stage and we do not want to prejudice the ongoing investigation.
"We are very much looking forward to being able to present all of the new evidence at a full appeal in due course.
"We believe when the whole truth comes out, the public will be given an entirely new perspective on what the Tommy Sheridan trial was really about.
"It is safe to say that many people will have their eyes opened for the first time."
Lawyer Aamer Anwar, who represented the former MSP during the trial, said: "Everyone is entitled to the presumption of innocence and it would be inappropriate to comment on Mr Coulson's detention today."
First Minister Alex Salmond has ruled out an inquiry into phone hacking.