Now, it is trying to succeed where other British behemoths like Tesco have failed in conquering the U.S.
Read MorePrimark extends Bangladesh factory collapse compensation
"This is sooner than we had anticipated, and whilst Primark will continue its measured approach to expansion, in our view this significantly increases the growth potential of Primark," retail analysts at Panmure Gordon wrote in a research note, which upgraded ABF from hold to buy as a result.
The company has signed a lease for around 70,000 square feet in the former Filene's Department Store site at Downtown Crossing in Boston, and should open there by the end of 2015. It is also mulling other openings on the north east U.S. coast.
The site is famed for the Filene's clock, a Boston landmark, which was preserved by the city after the department store was taken over by Macy's and its flagship closed.
Read MoreBig brands face scrutiny after factory collapse
Primark has recently been the target of controversy over the human cost of producing its bargain basement-priced clothes. More than 1,100 people were killed a year ago on Thursday following the collapse of a factory in Bangladesh producing clothes for the retailer and its competitors. Primark will pay out $12 million in total to victims and their families.
Mixed success for UK retailers in US
U.K. retailers trying to break into the U.S. have met with variable success. Supermarket giant Tesco confirmed it was exiting the U.S. last year, after its American chain of "Fresh & Easy" grocery stores failed to make a profit. This followed an earlier exit by upmarket rival, Marks & Spencer, which sold its U.S. supermarket business, Kings Super Markets, in 2006.
However, Arcadia-owned retailer Topshop is busy expanding in the U.S. It plans to open a 40,000-sq-foot flagship store in Manhattan in Autumn 2014, as well as stores in San Diego and Washington. Stores in Houston and Atlanta are slated for Spring 2015. Topshop has also agreed to sell its products through 42 Nordstrom stores in the U.S.
Read More Topshop sets out its store on 5th Avenue