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.
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British soldiers will join troops from some 30 countries who work in the country.
The demand comes after the Prime Minister urged a "grown up" relationship between her government and the devolved administrations.
The rapper failed to make it to London in time as he had problems with his passport.