After being selected for the Tipperary junior team in 1910, Dwan eventually captained the team to the All-Ireland title in 1915. By this stage he had also joined the Tipperary senior team. Dwan won his first Munster medal in 1916 before later winning his sole All-Ireland medal after Tipperary's defeat of Kilkenny in the final. He won a second Munster medal in 1922 after being joined on the team by his brother Billy.
In retirement from playing, Dwan served as a selector with the Tipperary senior team. He was a member of the selection committee for Tipperary's All-Ireland victories in 1949 and 1950.
Dwan died on 17 May 1980. At the time he was the last surviving member of the 1916 All-Ireland-winning team.