The field of remote sensing is nowadays faced with huge amounts of data. While this offers a variety of exciting research opportunities, it also yields significant challenges regarding both computation time and space requirements. In practice, the sheer data volumes render existing approaches too slow for processing and analyzing all the available data. This work aims at accelerating BFAST, one of the state-of-the-art methods for break detection given satellite image time series. In particular, we propose a massively-parallel implementation for BFAST that can effectively make use of modern parallel compute devices such as GPUs. Our experimental evaluation shows that the proposed GPU implementation is up to four orders of magnitude faster than the existing publicly available implementation and up to ten times faster than a corresponding multi-threaded CPU execution. The dramatic decrease in running time renders the analysis of significantly larger datasets possible in seconds or minutes instead of hours or days. We demonstrate the practical benefits of our implementations given both artificial and real datasets.