The couple are visiting at the request of Her Majesty's Government. Ahead of the visit Kensington Palace said: "They are looking forward to learning more about Ireland's history and experiencing its rich culture, as well as meeting the people who are shaping the country's future. Over the course of the trip, Their Royal Highnesses will meet the people of Dublin and will visit organisations which are central to Irish life."
The couple were warmly welcomed upon arrival.
The couple were deployed by the government to bolster Anglo-Irish relations and strengthen ties as Brexit unfolds. The Irish Times reports: "The Royal visit follows shortly after the successful trip to Cork and Kerry last month by Prince Charles and his wife, Camilla, Duchess of Cornwall. It was the latest in a series of visits to Ireland by Prince Charles. Queen Elizabeth II made the first Royal visit to Ireland by a reigning British monarch in a century in May 2011 - a trip hailed as hugely successful."
The arrivals marked the beginning of a new chapter for Meghan as a member of the Royal family - representing Her Majesty overseas.
Harry and Meghan's first port of call was Government Buildings where they were welcomed by Taoiseach Leo Varadkar.
Speaking before the royals arrived, the Taoiseach said: "It is the first visit they will have made overseas since they got married and even though they haven't officially visited Ireland before, I think they are going to be extremely welcome and I look forward to welcoming them. I think with the United Kingdom leaving Europe, we are really going to need to focus a lot more on bilateral relationships and visits of the President to the UK or members of the Royal family to Ireland to help cement that very close relationship between Britain and Ireland."
They were shown a plaque laid by Harry's great, great, great grandfather Edward VII.
Reporter Kevin Doyle shared the following information: "During their private meeting, Prince Harry suggested that the Irish Defence Forces could participate in the Invictus Games. Prince Harry also raised the issue of housing and homelessness with the Taoiseach. He repeatedly noted how much his father, Charles, likes visiting Ireland."
Meghan noted that she's an honorary member of 'the Phil' in Trinity and attended the same Chicago university (Northwestern) where Leo Varadkar's partner Matt works. Meghan was referring to her 2013 visit to Dublin, when she spoke at Trinity College's Philosophical Society, 'the Phil', where she was awarded with the Bram Stoker medal for Entertainment.
The Duke and Duchess signed the visitors book.
The Duchess very appropriately chose a forest green Givenchy ensemble for her first day in Dublin.
The hue was a lovely nod to the host country. We're seeing Meghan turn to her wedding dress designer, Clare Waight Keller, time and time again for important royal events. This look hit all the right notes, taking the Duchess from the airport to Government Buildings. It's a very versatile look.
Michelle notes Meghan's skirt is available in red at FarFetch and black at SSENSE. The $1,590 pencil skirt is described as "mid-length knit viscose-blend skirt in black. High-rise. Flap pockets at front. Concealed zip closure, raised seams, and central vent at back. Gold-tone hardware featuring carved logo detailing. Tonal stitching". Meghan's skirt is teamed with a fitted crew neck top.
Meghan carried a gorgeous new bag by Strathberry.
The Midi Tote in Tan Bridle Leather is described: "The Strathberry Midi Tote exudes feminine elegance with its understated styling and iconic Strathberry bar closure. Featuring two interior pockets, Strathberry branded hardware and a detachable and adjustable shoulder strap. Made in Spain using the finest bridle calf leather and microfiber lining with a suede like finish." Meghan's 'tan bridle' is sold out but the almost identical Tan is available. Michelle notes the only difference is Meghan's has visible stitching.
The talented Laura identified Meghan's pretty earrings as the Vanessa Tugendhaft Precious with Clover paved diamonds and 18K Pink Gold.
And a closer look at Meghan's suede pumps.