Online social networks convey rich information about geospatial facets of reality. However in most cases, geographic information is not explicit and structured, thus preventing its exploitation in real-time applications. We address this limitation by introducing a novel geoparsing and geotagging technique called Geo-Semantic-Parsing (GSP). GSP identifies location references in free text and extracts the corresponding geographic coordinates. To reach this goal, we employ a semantic annotator to identify relevant portions of the input text and to link them to the corresponding entity in a knowledge graph. Then, we devise and experiment with several efficient strategies for traversing the knowledge graph, thus expanding the available set of information for the geoparsing task. Finally, we exploit all available information for learning a regression model that selects the best entity with which to geotag the input text. We evaluate GSP on a well-known reference dataset including almost 10k event-related tweets, achieving $F1=0.66$. We extensively compare our results with those of 2 baselines and 3 state-of-the-art geoparsing techniques, achieving the best performance. On the same dataset, competitors obtain $F1 \leq 0.55$. We conclude by providing in-depth analyses of our results, showing that the overall superior performance of GSP is mainly due to a large improvement in recall, with respect to existing techniques.