The Celts did not always live in Ireland. They migrated there from mainland Europe in several waves, beginning in the 6th century BCE. They quickly became the dominant culture in Ireland, and their influence can still be seen in the language, music, and art of the country today.
So, while the Celts did not always live in Ireland, they have been there for over 2,500 years, and have become an integral part of the Irish culture.