We report the detection of a transiting planet around π Men (HD 39091), using data from the Transiting Exoplanet Survey Satellite (TESS). The solar-type host star is unusually bright (V = 5.7) and was already known to host a Jovian planet on a highly eccentric, 5.7 yr orbit. The newly discovered planet has a size of 2.04 ± 0.05 R⊕ and an orbital period of 6.27 days. Radial-velocity data from the High-Accuracy Radial-velocity Planet Searcher and Anglo-Australian Telescope/University College London Echelle Spectrograph archives also displays a 6.27 day periodicity, confirming the existence of the planet and leading to a mass determination of 4.82 ± 0.85 M⊕. The star's proximity and brightness will facilitate further investigations, such as atmospheric spectroscopy, asteroseismology, the Rossiter–McLaughlin effect, astrometry, and direct imaging
