Ab initio electronic structure calculations were performed to study the effect of V-doping on the structural, electronic, and magnetic properties of tin dioxide (Sn1-xVxO2, x: 0.042-0.125). Calculations have been performed using pseudopotentials and plane-wave and full potential linearized augmented plane-wave methods. State-of-the-art Heyd-Scuseria-Ernzerhof (HSE06) exchange-correlation hybrid functional and the Tran-Blaha-modified Becke-Johnson (TB-mBJ) exchange potential were employed. Our calculations showed that V4+ substitutionally replaces Sn4+ ions inducing a reduction of the volume cell of SnO2 and shortening of the metal-oxygen nearest neighbor bond lengths. Spin polarization at the V sites is predicted. Our results indicate that the magnetic ground state of the resulting system is paramagnetic. TB-mBJ and HSE06 accurately describe the experimentally reported dependence of the band gap with x. Our theoretical results for the hyperfine parameters at the Sn sites are in excellent agreement with Mössbauer experiments. Hyperfine parameters at the V sites are also presented.