But they are not the only major royals to have visited – Kate Middleton visited with her mother Carole Middleton back in 2007, during a brief split with Prince William.
The Queen has also paid a visit to the capital of the Irish Republic, in 2011.
But why not has Prince William not made a visit? The second-in-line to the British throne has visited northern Ireland, but never the Irish Republic.
Visiting the Republic of Ireland is not technically part of Prince William’s duties, as the future king of England.
The Republic of Ireland is not part of the Commonwealth, since it was automatically excluded when it broke away from Northern Ireland in 1949.
Nor is it part of the United Kingdom. Therefore, it it not a dependency of the British Crown.
The relationship between the royal family and the Republic of Ireland has not always been friendly.
Prince Philip’s uncle, Louis Mountbatten – whom Prince Louis is believed to be named after – was assassinated by the Irish Republican Army in Mullaghmore in 1979.
It took Queen Elizabeth half a century of her reign until she visited in 2011.
Her visit made her the first British monarch to visit the Republic of Ireland since 1911, when King George V visited.
It is believed Meghan and Harry’s visit is a further move to bolster relations between the two now separate nations.
They will visit Trinity College, the Famine Memorial and the Irish Emigration Museum as part of their visit next month.
They will also meet with Michael Higgins, The President of Ireland, and Leo Varadkar, The Taoiseach.
Meghan is married to Prince Harry, who is sixth in line for the British throne.
However, she cannot have the same title as Eugenie.
This is because she does not have royal blood, but instead has married into royalty.
“Rules governing the monarchy say only those with royal blood can use the title of Prince or Princess followed by their first name,” according to Sky News.
Therefore, Meghan will never be known as simply Princess Meghan.
She may, however, go by her official royal title, which is Her Royal Highness Princess Henry of Wales.