It was named on 6 August 1828 by Allan Cunningham, a botanist and explorer, after the River Teviot, Roxburghshire, Scotland. A plaque commemorating the naming is found at Coulson School in Coulson. In 2011, the Wyaralong Dam was opened. It dams the Teviot Brook between Allenview and Wyaralong at the southern end of the Flinders Peak Group.