The company, which trades as Penneys within Ireland, has signed a lease to open a store in Bratislava.
The store will form part of an extension to the Eurovea Shopping Centre, which is due to open in 2022.
The new shop will have 39,400 square foot of net retail space over two floors.
Paul Marchant, Primark CEO, said: "We are delighted to announce that we will open our first store in Slovakia, marking Primark's expansion into our 15th market.
"In the year of our 50th anniversary, we are incredibility proud to see our growth continue across Europe and the US."
The company has 376 stores across 12 markets, and will open its first stores in Poland and the Czech Republic next year.
"We are also excited to expand our store footprint in the US with stores opening in New Jersey and Florida in 2020, and further leases signed in Chicago and Philadelphia," Mr Marchant added.
The new store in Slovakia will mark Primark's entry into a fourth Central Eastern Europe market.
Primark opened its first store in the region in Ljubljana, Slovenia, in June of this year.
The company has also announced plans to open in Poland and the Czech Republic in 2020.
Primark was first established in Dublin in 1969 and employ over 75,000 people.
In the last financial year, the company opened 15 stores creating over 4,500 new jobs and received over 42,000 job applications for these stores.
