Comprehensive information on the timing and location of gene expression is fundamental to our understanding of embryonic development and tissue formation. While high-throughput in situ hybridization projects provide invaluable information about developmental gene expression patterns for model organisms like Drosophila, the output of these experiments is primarily qualitative, and a high proportion of protein coding genes and most non-coding genes lack any annotation. Accurate data-centric predictions of spatio-temporal gene expression will therefore complement current in situ hybridization efforts. Here, we applied a machine learning approach by training models on all public gene expression and chromatin data, even from whole-organism experiments, to provide genome-wide, quantitative spatio-temporal predictions for all genes. We developed structured in silico nano-dissection, a computational approach that predicts gene expression in >200 tissue-developmental stages. The algorithm integrates expression signals from a compendium of 6,378 genome-wide expression and chromatin profiling experiments in a cell lineage-aware fashion. We systematically evaluated our performance via cross-validation and experimentally confirmed 22 new predictions for four different embryonic tissues. The model also predicts complex, multi-tissue expression and developmental regulation with high accuracy. We further show the potential of applying these genome-wide predictions to extract tissue specificity signals from non-tissue-dissected experiments, and to prioritize tissues and stages for disease modeling. This resource, together with the exploratory tools are freely available at our webserver http://find.princeton.edu, which provides a valuable tool for a range of applications, from predicting spatio-temporal expression patterns to recognizing tissue signatures from differential gene expression profiles.