Born in Dublin, Meaney began studying acting at the age of fourteen. Upon completion of secondary school, he honed his skills at the Irish National Theatre's Abbey Theatre School of Acting before joining the company as a professional actor. After spending eight years touring throughout England as part of various acting companies, he made his television debut on the British television series Z Cars in 1978, which also featured Jeremy Kemp. He continued acting in various European productions, generally from the United Kingdom, but after training at the Pacific Conservatory of the Performing Arts (PCPA) he moved to New York in the mid-1980s to try his hand in Hollywood. He has since launched not only a successful TV career, but has become a highly recognized figure in feature film as well.