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We present a first-principles computational study of the nature and origin of ferromagnetism in Co-doped TiO2. We calculate the magnetic ordering and electronic properties as a function of the concentration and distribution of Co dopants and oxygen vacancies. We find that Co atoms prefer to substitute on neighboring sites of the Ti lattice, and show, using the well-established Goodenough-Kanamori-Anderson rules, that this leads to a ferromagnetic superexchange. We propose other semiconductor hosts in which the superexchange mechanism should lead to ferromagnetic coupling between the magnetic moments of neighboring transition metal dopants.