The Archbishop, who has served in his current role since December 2010, has been appointed by Pope Francis to serve in the Holy See Secretariat of State.
The President of the Bishops' Conference of Scotland, Archbishop Philip Tartaglia, congratulated his colleague on the appointment.
He said: "I thank His Excellency for the sensitive and helpful way he has fulfilled his role as the representative of the Holy Father to our Bishops' Conference and to the Catholic Church in Scotland.
"On behalf of the Bishops' Conference of Scotland and of the entire Catholic community, I assure him of our prayers as he embarks on his new mission."
Archbishop Antonio Mennini has had an extensive diplomatic career. He has also been the Pope's representative to Bulgaria, Russia and Uzbekistan. He is known in Italy as the priest who heard the final confession of murdered Prime Minister, Aldo Moro, in the 1970s.
He speaks seven languages and keeps a number of pet guinea pigs.