In order to simulate stratospheric phenomena, such as the Quasi-Biennial Oscillation (QBO), atmospheric general circulation models (GCM) require parameterizations of small-scale gravity waves (GW). In the tropics, the main source of GWs is convection, showing high spatial and temporal variability in occurrence and strength. In this study, we implement in the GCM ECHAM6 a source parameterization for GWs forced by convection. The GW source parameterization is based on the convective heating depth, convective heating rate, and the background wind. First, we show that the heating depth distribution of convective properties strongly influences the waves' source spectra. The strong sensitivity of spectral wave characteristics on heating property distributions highlights the importance of a realistic parameterization of convective processes in a GCM. Second, with the convection-based GW scheme as the unique source of GWs, the GCM simulates a QBO with realistic features. While the vertical extent of the easterly jet shows deficiencies, the wind speeds of the jet maxima and the variance of wind alteration show a clear improvement, compared to the standard model which employs a parameterization with constant, prescribed GW sources. Furthermore, the seasonality of the QBO jets downward progression is modeled more realistically due to the seasonality of physically based gravity wave sources.