Climate change is impacting the Arctic faster than anywhere else in the world. As a response, ecosystems are rapidly changing. As a result, we can expect rapid shifts in whale migration and habitat use concurrent with changes in human patterns. In this context, responsible management and conservation requires improved monitoring of whale presence and movement over large ranges, at fine scales and in near-real-time compared to legacy tools. We demonstrate that this could be enabled by Distributed Acoustic Sensing (DAS). DAS converts an existing fiber optic telecommunication cable into a widespread, densely sampled acoustic sensing array capable of recording low-frequency whale vocalizations. This work proposes and compares two independent methods to estimate whale positions and tracks; a brute-force grid search and a Bayesian filter. The methods are applied to data from two 260 km long, nearly parallel telecommunication cables offshore Svalbard, Norway. First, our two methods are validated using a dedicated active air gun experiment, from which we deduce that the localization errors of both methods are 100 m. Then, using fin whale songs, we demonstrate the methods' capability to estimate the positions and tracks of eight fin whales over a period of five hours along a cable section between 40 and 95 km from the interrogator unit, constrained by increasing noise with range, variability in the coupling of the cable to the sea floor and water depths. The methods produce similar and consistent tracks, where the main difference arises from the Bayesian filter incorporating knowledge of previously estimated locations, inferring information on speed, and heading. This work demonstrates the simultaneous localization of several whales over a 800 km area, with a relatively low infrastructural investment. This approach could promptly inform management and stakeholders of whale presence and movement and be used to mitigate negative human-whale interaction.