Before his plea bargain agreement, Tappin had denied attempting to sell batteries for surface-to-air missiles which were to be shipped from the US to Tehran via the Netherlands.
He was originally thought to have faced up to 35 years in jail if found guilty.
His guilty plea, to one count of the indictment, calls for a 33-month sentence which prosecutors have said they will not oppose him serving back in the UK.
More top news
Ofcom has been asked by cable giant Virgin Media to open a formal investigation into the way the Premier League sells its TV rights
The whole tooth: Five fascinating dental facts
Newcastle boss Alan Pardew's job is under no immediate threat despite a winless start to the Premier League season.