Mr Duncan is to be given a peerage so that he can serve in the government as a member of the House of Lords.
He will work alongside Scottish Secretary David Mundell, with a particular focus on the Brexit talks.
Opposition politicians were critical of the move, as Mr Duncan failed to win election in Perth and North Perthshire but still entered the government.
He lost out to the SNP's Pete Wishart by 21 votes, after a recount.
However, with the announcement of his peerage, it was confirmed that Mr Duncan will serve as parliamentary under-secretary of state in the Scotland Office.
Mr Duncan, who will step down as an MEP, said it was a "crucial time for Scotland" as the Brexit negotiations get under way. He has already said the Scottish government should have a seat at the table to "see exactly what is going on".
On his appointment he said: "Having worked in Brussels for many years as an MEP, and previously as an EU advisor to the Scottish Parliament, I understand how important it is that we build a new partnership with the EU, while making sure that whole of the UK gets the best possible deal, especially around crucial issues for Scotland such as fisheries, agriculture and energy.
"Working alongside Scottish Secretary David Mundell, and in close collaboration with the Scottish government, I look forward to playing a key role in helping build Scotland's economy and strengthen the union. We are in a strong position to deliver for Scotland."
Mr Wishart said the appointment of Mr Duncan was "so wrong" and "an insult to my constituents who recently rejected him", adding: "The abuse of the undemocratic House of Lords as a receptacle for cronies, donors and the defeated should no longer be accepted".
Scottish Conservative MEP Ian Duncan has been appointed as a Scotland Office minister.