They will also meet Secretary of State Theresa Villiers during engagements in Hillsborough Castle.
On Tuesday, the Royal couple will  visit the Giant's Causeway before travelling to Bushmills, County Antrim.
They will unveil a statue to Robert Quigg who won a Victoria Cross for bravery during the Battle of the Somme.
The Royal Couple will also attend a reception at Portrush Golf Club as guests of the Mayor of Coleraine and travel to Bellarena, County Londonderry, to unveil a plaque marking the opening of a new railway station.
The Queen and Duke of Edinburgh last visited Northern Ireland in June 2014.
The Queen and the Duke of Edinburgh will meet the first and deputy first ministers later on Monday during a two-day visit to Northern Ireland.