The KM3NeT Collaboration is building two underwater neutrino detectors: ARCA (Astronomy Research with Cosmic in the Abysses), deployed at 3500 m depth in the Ionian Sea, offshore from Sicily, aiming at the measurement of cosmic neutrino signals and at the detection of astrophysical neutrino sources; ORCA (Oscillation Research with Cosmic in the Abysses), deployed at 2500 m depth, offshore from Toulon, south of France, aiming at the measurement of the neutrino mass hierarchy. In both detectors, the direction and the energy of the interacting neutrinos are reconstructed through the water Cherenov technique. The Cherenkov light, induced by the charged particles resulting from the neutrino interaction, is measured by an array of optical sensors, installed on slender strings anchored on the sea bottom, called Detection Units (DUs). In order to effectively reconstruct particle tracks, the optical sensors coordinates must be known (in a known reference system) with an accuracy of a few tens of cm. Moreover, since the mechanical structures holding the optical sensors move under the effect of sea currents, their positions must be continuously monitored. In KM3NeT the positioning is performed using an array of piezo-electric acoustic receivers and a long baseline of several acoustic emitters and hydrophones installed in fixed positions on the seabed. All the elements of the acoustic positioning system are synchronized with the detector master clock. After measuring the range between each emitter and receiver, position of receivers is obtained in real time via multilateration. First results obtained with the current minimal infrastructure (2 DUs and 3 emitters in the ARCA field) demonstrate that the acoustic system already achieves a resolution close to 50 cm. The full stream of acoustic data from each receiver is sent onshore and can be also utilized for environmental monitoring purposes and bioacoustic research.