The High Altitude Water Cherenkov (HAWC) Gamma-Ray Observatory surveys the very high energy sky in the 300 GeV to $>100$ TeV energy range. HAWC has detected two blazars above $11sigma$, Markarian 421 (Mrk 421) and Markarian 501 (Mrk 501). The observations are comprised of data taken in the period between June 2015 and July 2018, resulting in a $sim 1038$ days of exposure. In this work we report the time-averaged spectral analysis for both sources above 0.5 TeV. Taking into account the flux attenuation due to the extragalactic background light (EBL), the intrinsic spectrum of Mrk 421 is described by a power law with an exponential energy cut-off with index $alpha=2.26pm(0.12)_{stat}(_{-0.2}^{+0.17})_{sys}$ and energy cut-off $E_c=5.1pm(1.6)_{stat}(_{-2.5}^{+1.4})_{sys}$ TeV, while the intrinsic spectrum of Mrk 501 is better described by a simple power law with index $alpha=2.61pm(0.11)_{stat}(_{-0.07}^{+0.01})_{sys}$. The maximum energies at which the Mrk 421 and Mrk 501 signals are detected are 9 and 12 TeV, respectively. This makes these some of the highest energy detections to date for spectra averaged over years-long timescales. Since the observation of gamma radiation from blazars provides information about the physical processes that take place in their relativistic jets, it is important to study the broad-band spectral energy distribution (SED) of these objects. To this purpose, contemporaneous data from the Large Area Telescope on board the {em Fermi} satellite and literature data, in the radio to X-ray range, were used to build time-averaged SEDs that were modeled within a synchrotron self-Compton leptonic scenario to derive the physical parameters that describe the nature of the respective jets.
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