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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South-east England will hold on to the cloud for longest, although the rain will gradually be easing through the afternoon.