US District Judge David Briones recommended that Mr Tappin should be allowed to serve his sentence in the UK but the decision ultimately rests with the US Bureau of Prisons, a spokeswoman for the court added.
He will commence his sentence at the Allenwood prison in Pennsylvania and must turn himself in to start the term by March 8.
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Some 66 people have been killed after the plane they were travelling on crashed in southern Iran.
The letter calls for an end to harassment, abuse, and impunity in a world "ripe for change".
Police say that anyone who sees Whitehouse should not approach him, but instead call them on 999 and quote incident 23 of 18 February.