We present LOFAR measurements of radio emission from extensive air showers. We find that this emission is strongly polarized, with a median degree of polarization of nearly 99%, and that the angle between the polarization direction of the electric field and the Lorentz force acting on the particles, depends on the observer location in the shower plane. This can be understood as a superposition of the radially polarized charge-excess emission mechanism, first proposed by Askaryan and the geomagnetic emission mechanism proposed by Kahn and Lerche. We calculate the relative strengths of both contributions, as quantified by the charge-excess fraction, for 163individual air showers. We find that the measured charge-excess fraction is higher for air showers arriving from closer to the zenith. Furthermore, the measured charge-excess fraction also increases with increasing observer distance from the air shower symmetry axis. The measured values range from (3.3± 1.0)% for very inclined air showers at 25 m to (20.3± 1.3)% for almost vertical showers at 225 m. Both dependencies are in qualitative agreement with theoretical predictions.