The X-ray source eRASSU J131716.9–402647 was recently identified from observations with Spectrum Roentgen Gamma (SRG)/eROSITA as a promising X-ray dim isolated neutron star (XDINS) candidate on the premise of a soft energy distribution, absence of catalogued counterparts, and a high X-ray-to-optical flux ratio. Here, we report the results of a multi-wavelength observational campaign with XMM-Newton, NICER and the FORS2 instrument at the ESO-VLT. We found in both the XMM-Newton and NICER data that the X-ray emission is strongly pulsed at a period of 12.757 s (pulsed fraction p_f = (29.1 ± 2.6)% in the 0.2–2 keV band). The pulse profile is double-humped, and the pulsed fraction increases with energy. The XMM-Newton and NICER epochs allow us to derive a 3σ upper limit of Ṗ ≤ 8 × 10⁻¹¹ s s⁻¹ on the spin-down rate of the neutron star. The source spectrum is well described by a purely thermal continuum, either a blackbody with kT ∼ 95 eV or a magnetised neutron star atmosphere model with kT ∼ 35 eV. Similarly to other thermally emitting isolated neutron stars, we found in either case strong deviations from the continuum, a broad absorption feature at energy ∼260 eV and a narrow one around 590 eV. The FORS2 instrument at ESO-VLT has not detected the optical counterpart (m_R > 27.5 mag, 5σ detection limit), implying an X-ray-to-optical flux ratio of 10⁴ at least. The properties of eRASSU J131716.9–402647 strongly resemble those of a highly magnetised isolated neutron star and favour an XDINS or high-B pulsar nature.