Air Force One touched down at Shannon Airport at around 4.45pm on Wednesday.
It will be Mr Trump's first visit to the Republic of Ireland as US president and comes just hours after he attended a ceremony to mark the 75th anniversary of the D-Day landings in Portsmouth.
He will hold a brief meeting with the Taoiseach (Irish prime minister) Leo Varadkar, before he goes to his golf resort in Doonbeg.
About a hundred people turned out to protest at the arrival of President Trump at the entrance to Shannon Airport.
They are unhappy about the president's policies on climate change and the use of Shannon Airport by the American military.
But elsewhere in Ireland, the President was greeted by the sight of Irish and American flags lining the streets as a warm welcome.
Issues including Huawei, bilateral relations, E3 visas, free trade and Brexit, are all expected to be raised.
Mr Trump's arrival in Ireland follows his three-day state visit to Britain which ended with his visit to Portsmouth and a goodbye from the Queen . His whirlwind tour began on Monday when he was greeted by her at Buckingham Palace and had tea with Charles and Camilla before enjoying a state banquet in the evening.
Day two involved talks with Prime Minister Theresa May at 10 Downing Street followed by a press conference. Then it was Mr Trump's turn to hold a lavish dinner at Winfield House - the official residence of Woody Johnson, the US ambassador to the UK - in Regent’s Park.
The president’s visit to Ireland is set to be largely private, with Mr Trump expected to base himself at the golf resort he owns in Doonbeg, Co Clare.
Rumours of a disagreement have been reported that focus on whether the meeting with Mr Varadkar would take place on Mr Trump’s property at Doonbeg – the president’s apparent preference – or on more neutral ground.
Irish authorities reportedly preferred nearby Dromoland Castle.
But Simon Coveney, Ireland’s deputy premier, said reports of a stand-off over locations were exaggerated and not true.
What will they discuss?
Mr Trump is expected to raise concerns about the Government’s stance on Chinese telecoms company Huawei when he meets Mr Vardakar.
The Chinese company has been at the centre of deepening tensions between Washington and Beijing, amid concerns that Huawei’s technology could be used by China to spy on sensitive data.
Last month the US effectively blacklisted Huawei, prompting Google to block the company from using its android apps on its devices.
A spokesman for Mr Varadkar said he and Mr Trump will also hold talks about bilateral relations, E3 visas, free trade and Brexit.
The two leaders are also expected to discuss support from the United States for the Northern Ireland political process.