The 50-year-old sang Tom Jones' hit I Who Have Nothing and has been hailed by many as 'the new Susan Boyle'.
Byrne has worked on the tills at the Ballyfermot store for the last 11 years. She is still a Tesco employee but is currently away while the show is broadcasting.
She has been performing in pubs and clubs for more than 20 years but told the judges she had been too nervous to try out for a TV show before. Simon Cowell told her he thought she had the best voice of everyone that had auditioned in Dublin that day.
A spokesman for Tesco Ireland said: "We are all very excited and we are all behind her."