The discovery sparked a major alert with thousands of staff and passengers evacuated and 28 flights cancelled on Tuesday.
The passenger in question - who has been released without charge - had placed his luggage in the scanner ahead of an outgoing domestic flight at around 2pm.
After security personnel spotted the shape on the display they shut down the machine and moved passengers away.
A subsequent swab of the passenger’s hand also found traces of what could have been an explosive substance, and the airport was shut down for more than three hours.
Sources denied earlier reports that the passenger was an explosives engineer - which would have explained the situation and cancelled the alert - and suggested he could provide no explanation for the positive test.
Staff are not allowed to open suspect packages to check for x-ray errors and bomb squad experts were called out to check the bag, with the airport re-opened at about 6pm.
Last night sources close to the investigation said that such errors with the x-ray machine were not uncommon, as staff have only a two dimensional view of luggage items.
One said: “Last time this happened, three years ago, it was a bag of Mini Creme Eggs which had burst open and a computer mouse placed beside them.
“On the x-ray machine viewer this looked like metal balls and the mouse a potential explosive device. Clearly the security guys can’t open it to have a look in case it sets it off.
“In this case it appears several items were laid out in such a way which gave security cause for concern, and when the passenger was swabbed he tested positive for a substance of some kind.”
Airline industry experts have said that basic tests often pick up other chemicals which resemble nitroglycerin, with sticky tape among such everyday items.
Ben Vogel, a leading security expert and editor of Jane’s Airport Review, told The Scotsman: “This happens fairly often around the world given: a) the general threat level to critical national infrastructure and b) the threat to aviation in particular.
“Airports and aircraft are perceived to be high-value targets for would-be terrorists, as Scotland knows only too well from Lockerbie and Glasgow.”
He added: “A surprising number of everyday items leave a residue resembling nitroglycerin, for example adhesive tape, playing cards, cigarette carton wrappers.
“This could trigger an alarm during a security search, depending on the sensitivity or probability of detection of the scanning equipment.
“Whether security staff at Edinburgh were over-cautious depends on your point of view – from the security agencies’ perspective, they can’t afford to take chances if scanning a bag/passenger triggers an alarm.”
Edinburgh Airport and Police Scotland have insisted that the closure of the airport was necessary to carry out the necessary checks.
In addition to the 28 cancellations, six flights were left on the tarmac with passengers waiting for three hours before being given the all-clear. Some passengers were critical of the delays but many praised airport staff for their handling of the situation.
Chief Inspector David Campbell, from Police Scotland’s border policing command, said that officers were “satisfied there isn’t, nor was there ever, any risk to the public”.
A spokesman for Edinburgh Airport added: “Our chief executive, Gordon Dewar, would like to thank all who worked into the night to ensure passengers were safe and the airport could return to normal as quickly as possible.
“Security is our number one priority and we will continue to work with our airport and wider partners to ensure all passengers can travel through Edinburgh Airport safely.”