He attended Christian Brothers' College, Kalgoorlie, and then moved to Perth to work as a clerk with the Commonwealth Taxation Office.
Teahan moved back to Kalgoorlie in 1932, setting up as a storekeeper and taxation consultant.
He was elected to the Boulder Municipal Council in 1938, and in 1944 was elected mayor.
Teahan contested Labor preselection for the 1948 Boulder by-election, but was defeated by Charlie Oliver.
He entered parliament at the 1954 Legislative Council election, defeating Sir Harold Seddon of the Liberal Party (the serving President of the Legislative Council).
Teahan was re-elected in 1960, but retired at the 1965 state election.