Those in shopping centres will open from Monday.
Penney's stores with street access will open at 10.30am tomorrow, while those in shopping centres will open on Monday.
Customer numbers in store will be limited, and additional security staff have been hired.
Every second till is closed to allow for social distancing, and fitting rooms are off limits for the moment.
Company CEO Paul Marchant has asked for cooperation from customers in adhering to social distancing measures.
He said: “We have really missed our customers in Ireland, and we are delighted to be back open from tomorrow, providing customers with the quality, affordable products they love from Penneys.
“While it might take a little longer to get into store, once inside, customers will find all their favourite Penneys products and plenty of choice as usual.
"We have worked hard to make sure that clear signage and extra help will be there to guide them through the changes we have made to allow for social distancing.
“We are also asking customers to respect the measures we have put in place to help ensure shopping at Penneys is an enjoyable, safe experience for everyone.”
