Now plans are being drawn up in Glasgow for a permanent memorial to the settlers and also those who arrived in the city from Scotland's Highlands and Islands during the 1840s Potato Blight that ravaged much of northern Europe.
The SNP in Glasgow has secured the support of its Labour rivals on the council for the tribute, which would bring the area into line with most other global cities to which the Irish emigrated during "An Gorta Mor".
Plans are at an embryonic stage, with backers insisting any memorial need not necessarily be a statue, and a garden among the early suggestions.
Locations mooted include the Broomielaw on the northern banks of the Clyde, where generations of Irish disembarked; and the People's Palace in the city's east end, close to the Calton area where many settled.
The SNP backers insist any memorial would celebrate the generosity of Glaswegians and the city's continued status as a destination for those fleeing hunger and famine across the globe.
The issue will be debated at the next meeting of the city's full council, after which a working group would develop plans for the style, location and funding for any memorial.
A motion put forward by the SNP councillor Feargal Dalton calls for recognition of "the significant cultural, economic and social impact of Ireland's An Gorta Mor and the Scottish Highland Potato Famine on the modern-day character of our great city" and "the efforts made by Glaswegians at the time to provide relief and sanctuary to those affected, a tradition that continues now as our city and its citizens continue to provide hope and assistance to those throughout the world affected by famine today".
The Partick councillor added: "The Great Hunger saw thousands arrive in Glasgow from both Ireland and the Highlands and Islands and they gave this city its Celtic characteristics. And when they arrived, Glaswegians gave generously.
"Yet, Glasgow is the one major world city where there continues to be a large Irish diaspora but has no permanent memorial. There's a general lack of awareness about one of the most defining times in our history."
Graeme Hendry, SNP leader at Glasgow City Council, said: "Once approved, the working group will hopefully be set up by the end of the year and then report by summer 2013.
"With the international context to the motion and visitors from all over the world coming to the city for the summer of 2014, it would be good to have it in place by then."
Councillor Gordon Matheson, leader of Glasgow City Council, said: "This is a good idea and has my full support."
The Irish who arrived in Scotland were among the poorest, as those who could scrape together more money headed to Canada and America. During 1848 the average weekly inflow of Irish into Glasgow was estimated at more than 1000, and the figure for January to April of that year was put at 42,860.
Some of the best-known Famine memorials are in the US, including the Irish Hunger Memorial in Manhattan, New York, and a national monument at Penns Landing, Philadelphia.
Danny Boyle, project manager at the Irish Heritage Foundation, said: "There was somewhere in the region of 30,000 Irish immigrants resident in Scotland before the onset of the An Gorta Mor in 1845-50. By 1878 there were 332,000. Irish immigration had a humongous impact on the personality and nature of the city.
"The multi-generational Irish community are part of the fabric of the city and the country as are all immigrants and refugees who have fled poverty, war, exploitation and famine in more recent times.
"It can stand as a testament to the sacrifices made by the city's collective people, understanding our heritage but looking to a positive future together."