The result of the by-election for the seat left by former Conservative council leader Keith Barrow was Green 518, Conservatives 367, Labour 95 and Lib Dem 81.
Natalie Bennett said: "Duncan's win in Shropshire is richly deserved. Like Greens up and down the country he has listened to the concerns of his community and demonstrated a genuine preparedness and readiness to challenge the status quo.
"The Green Party is going from strength to strength in the West Midlands, where increasing numbers of people are sick and tired of business-as-usual politics, and attracted to the Greens' blueprint for a fair economy, publically owned and run services and a safe climate."
Councillor Kerr said:"I would like to thank the people of South Oswestry for their support.
"Shropshire faces a very uncertain future with threats to all services from libraries and parks to care services for the elderly and young people all under threat.
"From my own knowledge and experience of 30 years in local government, I know there is an alternative to this dismantling of our society."
"I will be calling for policies which will rebuild the economy and vitality of our great town."