Bright and dark spatial solitons are predicted for biased photovoltaic photorefractive crystals, which are due to both the spatially nonuniform screening of the external electric field and the photovoltaic effect. These solitons differ form previously observed photorefractive spatial solitons in their properties. When external electric field is of a certain value, these solitons may be switched from bright to dark both by changing the polarity of the external electric field and by rotating the polarization of the light. In case the effect of the external bias field is much stronger than the photovoltaic effect and the latter can be neglected, these solitons are similar to screening solitons. In case the external bias field is absent, these solitons are similar to photovoltaic solitons in the open-circuit case.