Coulson, who served as David Cameron's communications chief between July 2007 and January 2011, was detained by officers from Strathclyde Police at his London home yesterday morning (May 30) and formally arrested later that day following his arrival in Glasgow for questioning.
The 44-year-old was questioned in relation to the evidence he gave at the perjury trial of former Scottish Socialist Party leader Tommy Sheridan in December 2010, and Coulson is now alleged to have himself committed perjury.
No date has yet been set for any future court appearance and officers from Operation Rubicon - which is investigating allegations of phone backing, perjury and data protection breaches in Scotland - said that a report will be submitted to the procurator fiscal, who will decide if Coulson is to face court proceedings.
A spokesperson for the Crown Office confirmed that Coulson has no legal obligation to stay in Scotland while he is on bail and is free to return home.
Coulson was also arrested last year as part of the separate Metropolitan Police investigation into alleged voicemail interception by newspapers. He has not been charged with any offence.