We demonstrate continuous tuning of the exciton binding energy in monolayer WS2 by means of an externally applied voltage in a field-effect transistor device. Using optical spectroscopy, we monitor the ground and excited excitonic states as a function of gate voltage and track the evolution of the quasiparticle band gap. The observed decrease of the exciton binding energy over the range of about 100 meV, accompanied by the renormalization of the quasiparticle band gap, is associated with screening of the Coulomb interaction by the electrically injected free charge carriers at densities up to 8×1012cm-2. Complete ionization of the excitons due to the electrical doping is estimated to occur at a carrier density of several 1013cm-2.