Estimating mobile signal strength accurately is a crucial task for network providers and their customers. However, current methodologies to estimate mobile signal strength present limitations in their practical implementation (i.e. physical based models), portability (i.e. spatial interpolation methods), simplicity and accuracy (i.e. path loss models). In this paper we present a novel approach that takes advantage of geospatial Big Data and advanced Artificial Intelligence to predict mobile signal strength at scale. Particularly, we used open access geo-spatial information about weather, tree coverage, land use, imperviousness, altitude and network infrastructure (i.e. a total of 174 features) to train and test uncertainty-aware artificial neural networks to predict mobile signal strength on data from the NetBravo crowdsourcing platform across all the United Kingdom (UK). Our model scored a best performance of 7.9 (standard deviation of 0.2) dBm for Root Mean Squared Error and 5.7 (standard deviation of 0.4) dBm for the Mean Absolute Error. Feature importance analysis showed that mobile cell tower characteristics and geospatial features showing the distribution of imperviousness and tree cover density over the line of sight between the mobile cell tower and the receiver as well as relative humidity were among the top 20 most important features.