To manage the COVID-19 epidemic effectively, decision-makers in public health need accurate forecasts of case numbers. A potential near real-time predictor of future case numbers is human mobility; however, research on the predictive power of mobility is lacking. To fill this gap, we introduce a novel model for epidemic forecasting based on mobility data, called mobility marked Hawkes model. The proposed model consists of three components: (1) A Hawkes process captures the transmission dynamics of infectious diseases. (2) A mark modulates the rate of infections, thus accounting for how the reproduction number R varies across space and time. The mark is modeled using a regularized Poisson regression based on mobility covariates. (3) A correction procedure incorporates new cases seeded by people traveling between regions. Our model was evaluated on the COVID-19 epidemic in Switzerland. Specifically, we used mobility data from February through April 2020, amounting to approximately 1.5 billion trips. Trip counts were derived from large-scale telecommunication data, i.e., cell phone pings from the Swisscom network, the largest telecommunication provider in Switzerland. We compared our model against various state-of-the-art baselines in terms of out-of-sample root mean squared error. We found that our model outperformed the baselines by 15.52%. The improvement was consistently achieved across different forecast horizons between 5 and 21 days. In addition, we assessed the predictive power of conventional point of interest data, confirming that telecommunication data is superior. To the best of our knowledge, our work is the first to predict the spread of COVID-19 from telecommunication data. Altogether, our work contributes to previous research by developing a scalable early warning system for decision-makers in public health tasked with controlling the spread of infectious diseases.