The group said that the people of South Africa have shown they are "tired of corruption, maladministration."
The African National Congress (ANC) has lost power in Johannesburg for first time, it has been in charge since the ending of apartheid more than 20 years ago.
Agenzia Fides has reported the bishops said: "This peaceful elections auger well for the future stability of our political system."
They praised democracy and thanked God "for the growing maturity of our democracy and we praise all political parties who have accepted the outcome".
The bishops concluded by saying: "Our Country faces huge problems of social trauma; unemployment, inequality, racism, violence, drugs abuse and family breakdown".
They asked that those in power now look forward and help heal wounds and bring the change that the people of South Africa have asked for.
