The aircraft touched down shortly after 8.20am on Saturday, with Trump arriving in Ireland for a series of political engagements in Dublin before travelling to Doonbeg, Co Clare.
A crowd had gathered at a nearby viewpoint from the early hours in the hope of watching the distinctive red, white and blue presidential aircraft arrive.
Trump was welcomed at Dublin Airport by Tánaiste Simon Harris, who said he was pleased to represent the Irish Government as the US president arrived.
Mr Harris said he had a brief conversation with Trump beside Air Force One and recalled previous discussions between the two men, including a phone call following Trump's election as US president.
The Tánaiste said Trump was looking forward to travelling to Doonbeg, where he owns a golf resort, and highlighted the personal significance of the trip for the president's family.
Trump is expected to begin his Dublin programme with a meeting with President Catherine Connolly at Áras an Uachtaráin in the Phoenix Park. He will then meet Taoiseach Micheál Martin at Farmleigh before attending further engagements at the US ambassador's residence.
The presidential arrival has also prompted a major security operation, with road closures and restrictions expected around Dublin Airport, across the capital and later in Co Clare.
Air Force One itself has attracted attention. Trump travelled to Ireland aboard a Boeing 747-8 gifted by Qatar's royal family, which has been temporarily adapted for presidential use.
The aircraft is being used as an interim Air Force One while new presidential aircraft face delays. Trump has previously said the jet will undergo further security upgrades.
For the Irish Government, however, the arrival is about more than the spectacle surrounding the presidential aircraft.
Mr Harris said the visit provides an opportunity to underline the longstanding political, economic and personal connections between Ireland and the United States. He pointed to the large number of American companies employing people in Ireland and Irish businesses operating in the US.
With Air Force One now on Irish soil, Trump's programme will move from the highly visible arrival at Dublin Airport to a series of diplomatic engagements before the president heads west to Doonbeg.
