TOI-1899b is a rare exoplanet, a temperate warm Jupiter orbiting an M-dwarf, first discovered by Canas et al. (2020) from a TESS single-transit event. Using new radial velocities (RVs) from the precision RV spectrographs HPF and NEID, along with additional TESS photometry and ground-based transit follow-up, we are able to derive a much more precise orbital period of P=29.090312_-0.000035_^+0.000036^days, along with a radius of Rp=0.99{+/-}0.03RJ. We have also improved the constraints on planet mass, Mp=0.67{+/-}0.04MJ, and eccentricity, which is consistent with a circular orbit at 2{sigma}(e=0.044_-0.027_^+0.029^). TOI-1899b occupies a unique region of parameter space as the coolest known (Teq~380K) Jovian-sized transiting planet around an M dwarf; we show that it has great potential to provide clues regarding the formation and migration mechanisms of these rare gas giants through transmission spectroscopy with JWST, as well as studies of tidal evolution.