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
Dorset's Weymouth Beach has been named the UK's best by travellers, with Fistral Bay, Cornwall, coming in second place.
Wednesday will be a cloudy but mild day across southern England and Wales with outbreaks of rain
A diplomat from the North Korean embassy in Kuala Lumpur is being sought over the death of Kim Jong-nam.