Pulsations from the high-mass X–ray binary AX J1910.7+0917 were discovered during Chandra observations performed in 2011. We report here more details on this discovery and discuss the source nature. The period of the X-ray signal is P = 36200 ± 110 s, with a pulsed fraction, PF, of 63 ± 4 per cent. Given the association with a massive B-type companion star, we ascribe this long periodicity to the rotation of the neutron star (NS), making AX J1910.7+0917 the slowest known X-ray pulsar. We also report on the spectroscopy of XMM−Newton observations that serendipitously covered the source field, resulting in a highly absorbed (column density almost reaching 10²³ cm⁻²), power-law X-ray spectrum. The X-ray flux is variable on a time-scale of years, spanning a dynamic range ≳ 60. The very long NS spin period can be explained within a quasi-spherical settling accretion model that applies to low luminosity, wind-fed, X-ray pulsars.