We report on the precise radial velocity follow-up of TOI-544 (HD 290498), a bright K star (V = 10.8), which hosts a small transiting planet recently discovered by the Transiting Exoplanet Survey Satellite (TESS). We collected 122 high-resolution High Accuracy Radial velocity Planet Searcher (HARPS) and HARPS-N spectra to spectroscopically confirm the transiting planet and measure its mass. The nearly 3-yr baseline of our follow-up allowed us to unveil the presence of an additional, non-transiting, longer-period companion planet. We derived a radius and mass for the inner planet, TOI-544 b, of 2.018 ± 0.076 R⊕ and 2.89 ± 0.48 M⊕, respectively, which gives a bulk density of $1.93^{+0.30}_{-0.25}$ g cm-3. TOI-544 c has a minimum mass of 21.5 ± 2.0 M⊕ and orbital period of 50.1 ± 0.2 d. The low density of planet-b implies that it has either an Earth-like rocky core with a hydrogen atmosphere, or a composition which harbours a significant fraction of water. The composition interpretation is degenerate depending on the specific choice of planet interior models used. Additionally, TOI-544 b has an orbital period of 1.55 d and equilibrium temperature of 999 ± 14 K, placing it within the predicted location of the radius valley, where few planets are expected. TOI-544 b is a top target for future atmospheric observations, for example with JWST, which would enable better constraints of the planet composition.