Teahan was born in 1905 at Glountane, South County Kerry, Ireland. His father died when he was very young. His mother was a popular singer, while his extended family contained many musicians who played at dances in the neighbourhood. Among his neighbours were eminent musicians Padraig O'Keeffe, who taught him music at Glountane School, and Johnny O'Leary. O'Keeffe's father, Seán, and sister Nora Carmody also taught him at that school. In 1928 he emigrated to the United States and settled in Chicago. Over the next few years, during the depression, he returned to Ireland, but set off again for Chicago in 1933. He started work with Illinois Central in 1936 and remained with them until he retired in 1970.
From 1943 to 1964 he played concertina and button accordion three nights a week at the major Irish dance-halls in Chicago, as well as at weddings and cultural events. During this time he also toured with Roche's School of Dancing. In the 1970s he performed with Mary McDonagh (piano), Maida Sugrue (vocals) and Una McGlwe (fiddle). In 1978, in recognition of his special contributions, he was voted Irishman of the Year by the Harp and Shamrock club.
After he retired from Illinois Central he played in Chicago with the Dayhills Irish Band.
He received the nickname "Cuz" because he helped out newly arrived Irishmen by telling them where to find accommodation, work, etc. He would say: "Tell them I'm your cousin".
- The Dayhills' Mom's Favorite: Irish Music in America, Biscuit City BC1308.
- Terry Teahan and Gene Kelly: Old Time Irish Music in America, 1977, Topic 12TS352.
- Irish Music in Chicago
- Kerry Music (Mulligan LUN 019)
- Cuz – a tribute to Terry 'Cuz' Teahan by Niamh Ní Charra, Imeartas Records IMCD004. Includes special guests Seamus Begley, Liz Carroll, Mick Moloney, Donal Murphy and Tommy 0 Sullivan.