The Queen was invited to Ireland by the Republic’s President, Mary McAleese, who will formally welcome the monarch at her home in Dublin’s Phoenix Park.
The Queen will attend events at Trinity College Dublin, the National War Memorial Gardens in Islandbridge and at Croke Park stadium.
Croke Park is the home of Gaelic football where, in 1920 during the Irish War of Independence, British forces fired into the crowd at a match, killing 14 spectators and players.
There are also plans for the Queen and Prince Philip to visit the Irish National Stud in Kildare, as well as the Rock of Cashel in County Tipperary, and a technology park in Cork.
The Queen is set to make a speech at a state dinner at Dublin Castle.
Asked about the threat of a dissident republican attack, Mrs May told the BBC: “We constantly live looking at the issue of the threat of terrorism.
“We know regarding Northern Irish-related terrorism there have been a number of attempted attacks earlier this year and there was of course the death of Pc Ronan Kerr.
“What was significant about that was the response from the Taoiseach…that incidents like that are not blowing us off the course of democracy in Northern Ireland,” she added.
She said the visit was a historic moment and was an important stage in marking the relationship between the two countries.