"From India to Ireland...strengthening ties and deepening cooperation," Modi tweeted as soon as he landed here.
He is scheduled for a "tete-a-tete" with Taoiseach (Prime Minister) Enda Kenny at the Government Buildings in Dublin City Centre followed by a working luncheon hosted by Kenny in honour of Modi, the first Indian Premier to visit the country in almost 60 years.
"We hope to further develop strong people-to-people and economic ties with Ireland in the years to come," Modi had said in a Facebook post in reference to the visit.
Relations between India and Ireland date back to independence and in 2013, the total trade in goods and services was pegged at euro 2.48 billion.
The key items of Irish export include computer hardware and software, pharmaceuticals and chemicals, food and machinery.
Indian exports to Ireland cover textiles, garments and clothing accessories, pharmaceuticals, light engineering goods and chemicals.
Major Indian companies with a presence in Ireland include pharma majors like Wockhardt, Sun Pharma and Reliance Genemedix and information technology firms like FirstSource, Tata Consultancy Services (TCS), HCL and Wipro.
Following the government-level interactions, the Prime Minister will interact with the Indian community in Ireland at a special event being hosted at Hotel Double Tree Hilton in Dublin.
Ireland is home to around 26,000 persons of Indian origin, of which around 17,000 are Indian citizens.
The bulk of the community is in the healthcare sector, working as doctors and nurses, with information technology and engineering among some of the other sectors.
The country is also fast emerging as a significant destination for Indian students seeking higher education, particularly in post-graduate, doctoral and post-doctoral courses in these particular fields.
"This is a very historic visit and there are lots of expectations from Mr Modi.We are confident the PM is the right person to trust to increase foreign investments for India," said Lalubhai Parekh, president of the Overseas Friends of BJP (OFBJP).
From Dublin, Modi sets off for New York this evening to address a UN Sustainable Development Summit and participate in a summit on peacekeeping being hosted by US President Barack Obama.
He then travels on to the West Coast of the US, where he will address the Indian community in the Silicon Valley and hold meetings with top tech CEOs as part of this two-nation, three-city tour which concludes on September 29.
The last Indian prime minister to visit Ireland was Jawaharlal Nehru in 1956.