We report the discovery of two warm sub-Neptunes transiting the bright (G = 9.5 mag) K-dwarf HD 15906 (TOI461, TIC 4646810). This star was observed by the Transiting Exoplanet Survey Satellite (TESS) in sectors 4 and 31, revealing two small transiting planets. The inner planet, HD 15906 b, was detected with an unambiguous period but the outer planet, HD 15906 c, showed only two transits separated by similar to 734 d, leading to 36 possible values of its period. We performed follow-up observations with the CHaracterising ExOPlanet Satellite (CHEOPS) to confirm the true period of HD 15906 c and improve the radius precision of the two planets. From TESS, CHEOPS, and additional ground-based photometry, we find that HD 15906 b has a radius of 2.24 +/- 0.08 R-circle plus and a period of 10.924709 +/- 0.000032 d, whilst HD 15906 c has a radius of 2.93(-0.06)(+0.07) R-circle plus and a period of 21.583298(-0.000055)(+0.000052) d. Assuming zero bond albedo and full day-night heat redistribution, the inner and outer planet have equilibrium temperatures of 668 +/- 13 K and 532 +/- 10 K, respectively. The HD 15906 system has become one of only six multiplanet systems with two warm (less than or similar to 700 K) sub-Neptune sized planets transiting a bright star (G <= 10 mag). It is an excellent target for detailed characterization studies to constrain the composition of sub-Neptune planets and test theories of planet formation and evolution.