This letter presents the first calculation of the exciton binding energy (Ex) and oscillator strength (os) for quantum dots in type II semiconductor systems. These structures consist of a spherical dot of one semiconductor embedded in a second semiconductor. As in the type II exciton systems in quantum wells, the electron is confined in one semiconductor and the hole in the other due to band line-ups in the two materials which make this arrangement energetically favourable. We use a variational calculation where the wavefunction of the particle confined to the dot is a spherical Bessel function and the wavefunction of the other particle is a generalized Fang-Howard wavefunction allowing correlation with the confined particle. We have considered the GaAs/AlAs system where the electron is confined in the X state in the AlAs while the hole is confined in the GaAs dot which is indirect in both real and k space for a dot radius of less than 56 angstrom. We compare Ex in the type II dot to Er, the binding energy of a bulk hydrogenic impurity in the AlAs. We find that for the case of infinite barriers Ex <Er. For the finite barrier case with wavefunction leakage into the dot, Ex >> Er due to the effect of the overlapping electron and hole wavefunctions within the dot. Although Ex is always smaller for type II than for the corresponding type I systems (using the masses of the type II system) the values for a type II dot system are vastly larger than those for a type II quantum well system due to the extra correlation in the other two confined dimensions. The Ex of the type II GaAs/AlAs system are comparable to the Ex of the type I GaAs/AlxGa1-xAs system (with the electron mass being that of the Γ valley) for a gt; 30 angstrom where a is the radius of the dot.