The visit, at the request of the British government, is expected to attract a lot of media attention.
Harry and Meghan are scheduled to attend a summer garden party Tuesday night at Glencairn House, the British ambassador's residence.
The Duke of Cambridge, alongside wife Kate Middleton-who broke her maternity leave for a surprise appearance at a service for the Royal Air Force centenary at Westminster Abbey (the site of her 2011 royal wedding)-couldn't help but let a smirk slip on Tuesday morning.
Then the couple will have a whole day of activities in Dublin on Wednesday, including a trip to Trinity College, to see the Book of Kells, considered one of Ireland's greatest cultural treasures.
Their final engagement in Dublin will be meeting with young people who take part in free coding workshops at Dogpatch Labs.
Even before leaving for Ireland, it has been a busy week for the newlyweds.
Queen Elizabeth and senior royals watched nearly 100 aircraft, from World War Two Spitfires to the newest stealth fighter jet fly over Buckingham Palace on Tuesday in a celebration to mark the 100th anniversary of Britain's Royal Air Force.
Other guests at the posh do were Prince Charles and Camilla, as well as the Duke and Duchess of Cambridge with their three youngsters, Prince George, 4, Princess Charlotte, 3 - and of course Prince Louis, eleven weeks.
More than 2,200 people packed out Westminster Abbey for the service, with dignitaries including Defence Secretary Gavin Williamson and the Archbishop of Canterbury Justin Welby attending.