He has arrived amid what has been described as one of the biggest security operations ever implemented by the Irish police service.
Mr Trump was greeted by Ireland's deputy premier Simon Harris at Dublin Airport.
He is expected to meet President Catherine Connolly, a long-standing critic of the US president, at her official residence Áras an Uachtaráin in Dublin's Phoenix Park, before a nearby engagement with Irish Premier Micheál Martin at the Farmleigh Estate.
Former Irish premiers Bertie Ahern and Enda Kenny were among hundreds of guests arriving at the residence of the US ambassador to Ireland, Edward Walsh, ahead of Mr Trump's arrival.
Prominent business leaders, including Ryanair boss Michael O'Leary, and entertainer Michael Flatley, were also among those expected to attend as Mr Trump will make a speech in a marquee set up in the grounds of the historic property at Deerfield in Phoenix Park, which is decked out with American flags.
Sound checks have included the playing of some of Mr Trump's favourite songs, including the Village People's YMCA, and his traditional walk-out song God Bless The USA by Lee Greenwood.
Mr Trump will later travel across the country to his golf resort in Doonbeg, Co Clare, which is hosting the Irish Open.
Prominent business leaders, including Ryanair boss Michael O'Leary, and entertainer Michael Flatley, were also among those expected to attend as Mr Trump will make a speech in a marquee set up in the grounds of the historic property at Deerfield in Phoenix Park, which is decked out with American flags.
Sound checks have included the playing of some of Mr Trump's favourite songs, including the Village People's YMCA, and his traditional walk-out song God Bless The USA by Lee Greenwood.
Mr Trump will also travel across the country to his golf resort in Doonbeg, Co Clare, which is hosting the Irish Open.
Mr Martin has said he was looking forward to welcoming Mr Trump to Ireland and "discussing the many issues of mutual interest and reaffirming the strong economic, cultural and people-to-people ties between Ireland and the United States".
"His visit comes during a remarkable sporting summer for Ireland and the United States and this weekend's Irish Open at Trump International Doonbeg will be a fitting conclusion to an outstanding season of sport, and I hope we will see an Irish winner lifting the trophy on Sunday," Premier Martin said.
A number of protests against Mr Trump's visit have been planned.
Garda Commissioner Justin Kelly said peaceful protest would be facilitated as much as possible, but there would be "no tolerance" for public disorder or attempts to impact "critical movements" of the US president.
"We have robust policing plans in place and will arrest and prosecute those committing offences," he said, adding that water cannon would be "on standby" but he hoped they would not be needed.
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