The exchange took place in a brief and informal 30 minute audience at the Vatican today.
The queen and her husband, the Duke of Edinburgh, was on the ground in Italy for less than five hours before returning to the United Kingdom on a private jet.
It was the first time Queen Elizabeth met Pope Francis and she took with her on the plane home a gift for the royal grandson. Pope Francis handed the queen a precious stone globe with a cross on it for Prince George, who is about to depart on his first overseas trip to Australia and New Zealand.
The Queen's Papal Meetings Through the Years
The queen was given an antique parchment, which dates back to May 1679 with an "Urbi et Orbi" message by Cardinal Cesare Facchinetti. The pope traditionally gives a "urbi et orbi" message - meaning "to the city and the world" - at Easter and Christmas.
The queen gave the pope a hamper of what the Vatican said was "jams and drinks" produced on lands owned by the royal family. One of the drinks was a bottle of whiskey from Balmoral.
As a pair, the queen and the pope are leaders to billions of people around the world.