In their TV statement the coup leaders said they were cancelling the results of the election and dissolving "all the institutions of the republic".
The country's borders had been closed "until further notice", they added.
It came after Gabon's electoral commission said Mr Bongo had won just under two-thirds of the votes in Saturday's election, which the opposition argued was fraudulent.
One of the soldiers said they had "put an end to the current regime" because of "irresponsible, unpredictable governance resulting in a continuing deterioration in social cohesion that risks leading the country into chaos".
