It is the first Irish store of the brand and is located on College Green in the city centre.
It is employing 300 people on a full and part-time basis.
It is reported the company has signed a 100 year lease which is worth €750,000 annually.
The Ohio-based chain is floated on the New York Stock Exchange and has shops across Europe, the US, Canada and Asia.
Long queues
Dozens of people have been queuing in the cold since early this morning to get into the flagship store.
The opening of the Dublin outlet is also being promoted on the global homepage of the retailers website.
These A&F fans arrived at the Dublin store just after 6.30am and are at the top of the queue.