The 44-year-old was detained in London this morning by officers from Strathclyde Police.
Mr Coulson gave evidence in the former Scottish Socialist MSP’s perjury trial at the High Court in Glasgow in December 2010.
A Strathclyde Police spokesman said: “Officers from Strathclyde Police Operation Rubicon detained a 44-year-old man in London this morning under section 14 of the Criminal Procedures Scotland Act on suspicion of committing perjury before the High Court in Glasgow.
“It would be inappropriate to comment any further at this time.”
It is understood Coulson is on his way to Glasgow.
Operation Rubicon detectives have been looking at whether certain witnesses lied to the court during Sheridan’s trial as part of an investigation into phone hacking in Scotland.
The trial led to Sheridan’s conviction in December 2010. He has since been freed after serving just over a year of a three-year sentence.
Mr Coulson was called to give evidence at Sheridan’s trial because he was editor of the News of the World between 2003 and 2007, when it had published allegations about Sheridan’s private life.
Sheridan was awarded £200,000 in damages after winning the civil case, but a jury at the High Court in Glasgow found him guilty of lying about the now-defunct tabloid’s claims that he was an adulterer who visited a swingers’ club.
Mr Coulson, then employed by Downing Street as director of communications, told the trial in December 2010 he had no knowledge of illegal activities by reporters while he was editor of the News of the World.
He also claimed: “I don’t accept there was a culture of phone hacking at the News of the World.”