The structural and electronic properties of BiCoO3 under high pressure have been investigated. Synchrotron X-ray and neutron powder diffraction studies show that the structure changes from a polar PbTiO3 type to a centrosymmetric GdFeO3 type above 3 GPa with a large volume decrease of 13% at room temperature revealing a spin-state change. The first-order transition is accompanied by a drop of electrical resistivity. Structural results show that Co3+ is present in the low spin state at high pressures, but X-ray emission spectra suggest that the intermediate spin state is present. The pressure temperature phase diagram of BiCoO3 has been constructed enabling the transition temperature at ambient pressure to be estimated as 800-900 K.