Lawyers for Tappin, who ran his own export company for 35 years, said his ordeal began when he was approached by Robert Gibson, a US client, to export a shipment of batteries, from the US to the Netherlands.
Tappin said he was told the batteries, reportedly worth around $5,000 each were going to be used in the car industry.
He was then put in touch with a company called Mercury Global Enterprises, which he said he believed would provide documents for an export licence for the batteries.
But the company was a front for undercover US customs agents set up to trap those interested in breaking the arms embargo to Iran.
Gibson in the meantime had been arrested in the US and was accused of acting as a "co-operating defendant".
At a press conference in central London on Tuesday, Tappin said Mercury Global Enterprises "exists solely to ensnare unsuspecting importers".
"When negotiating with me, and when I raised my concerns about the licence agreement they assured me that 'this would not be a problem', however the same agents have been relied upon to accuse me of being responsible for not obtaining the licences.
"They misled me by sending me paperwork which clearly stated 'no license
required'," he said.
The businessman said he was willing to face a trial in the UK, but not the US.
"I live here with my family and the alleged crimes were committed here."
Extradition treaty slammed
The case has led to renewed criticism of the British extradition agreement with the US.
Shami Chakrabarti, director of the human rights organisation Liberty based in London said it was up to authorities in a British court to prove the allegations against Tappin.
"If Mr Tappin really has been up to no good in Orpington, let the authorities come up with hard evidence in a British court.
"Until the Act is amended to put fairness back in the system, no one who indulges in foreign holidays, business dealings or mere use of the internet is safe from being shipped off like freight on the basis of allegations from around the world."
Tappin's case has been taken up by Karen Todner, the solicitor representing Gary McKinnon, who faces being extradited over allegations he hacked into Pentagon computers.