The theory of solitary topographic Rossby waves (modons) in a uniformly rotating two-layer ocean over a constant slope is developed. The modon is described by an exact, form-preserving, uniformly translating, horizontally localized, nonlinear solution to the inviscid quasi-geostrophic equations. Baroclinic topographic modons are found to translate steadily along contours of constant depth in both directions: either with negative speed (within the range of the phase velocities of linear topographic waves) or with positive speed (outside the range of the phase velocities of linear topographic waves). The lack of resonant wave radiation in the first case is due to the orthogonality of the flow field in the modon exterior to the linear topographic wave field propagating with the modon translation speed, that is impossible for barotropic modons. Another important property of a baroclinic topographic modon is that its integral angular momentum must be zero only in the bottom layer; the total angular momentum can be non-zero unlike for the beta-plane modons over flat bottom. This feature allows modon solutions superimposed by intense monopolar vortices in the surface layer to exist. Explicit analytical solutions for the baroclinic topographic modons with piecewise linear dependence of the potential vorticity on the streamfunction are presented and analysed.