We report the discovery and characterization of a transiting warm sub-Neptune planet around the nearby bright (V = 8.75 mag, K = 7.15 mag) solar twin HD 183579, delivered by the Transiting Exoplanet Survey Satellite (TESS). The host star is located 56.8 ± 0.1 pc away with a radius of R* = 0.97 ± 0.02 R⊙ and a mass of M* = 1.03 ± 0.05 M⊙. We confirm the planetary nature by combining space and ground-based photometry, spectroscopy, and imaging. We find that HD 183579b (TOI-1055b) has a radius of Rp = 3.53 ± 0.13 R⊕ on a 17.47 day orbit with a mass of Mp = 11.2 ± 5.4 M⊕ (3σ mass upper limit of 27.4 M⊕). HD 183579b is the fifth brightest known sub-Neptune planet system in the sky, making it an excellent target for future studies of the interior structure and atmospheric properties. By performing a line-by-line differential analysis using the high resolution and signal-to-noise ratio HARPS spectra, we find that HD 183579 joins the typical solar twin sample, without a statistically significant refractory element depletion.