We report measurements of the 6${\mathit{p}}^{2}$${\mathit{P}}_{1/2}$ and 6${\mathit{p}}^{2}$${\mathit{P}}_{3/2}$ state lifetimes in the $^{133}\mathrm{Cs}$ atom with precisions of 0.23% and 0.27%, respectively. The results are important to the interpretation of the next generation of parity nonconservation experiments in atomic cesium. A diode laser was used to selectively excite a fast beam of neutral cesium atoms. The decay in flight of the fluorescence was observed with photon-counting detectors. The lifetime results are 34.934\ifmmode\pm\else\textpm\fi{}0.094 ns for the 6${\mathit{p}}^{2}$${\mathit{P}}_{1/2}$ state and 30.499\ifmmode\pm\else\textpm\fi{}0.070 ns for the 6${\mathit{p}}^{2}$${\mathit{P}}_{3/2}$ state. We present comparisons with previous measurements and with relativistic many-body calculations of alkali-metal-atom transition matrix elements.