The force arrested the man on Thursday at Birmingham Airport on suspicion of terror offences.
His arrest was in connection with inquiries into the IRA bomb detonation in Manchester city centre on June 15 1996.
The 3,300lb bomb caused massive damage and more than 200 injuries, but no fatalities.
On Saturday the police said he had been released without charge on Friday night.
The force has asked anyone who had been affected by the bombing who had not been contacted by police to access the Major Incident Portal at mipp.police.uk/operation/06GMP20S33-PO1.