We present the stellar calibrator sample and the conversion from instrumental to physical units for the 24{mu}m channel of the Multiband Imaging Photometer for Spitzer (MIPS). The primary calibrators are A stars, and the calibration factor based on those stars is 4.54x10^-2^MJy/sr/(DN/s), with a nominal uncertainty of 2%. We discuss the data reduction procedures required to attain this accuracy; without these procedures, the calibration factor obtained using the automated pipeline at the Spitzer Science Center is 1.6%+/-0.6% lower. We extend this work to predict 24{mu}m flux densities for a sample of 238 stars that covers a larger range of flux densities and spectral types. We present a total of 348 measurements of 141 stars at 24{mu}m. This sample covers a factor of ~460 in 24{mu}m flux density, from 8.6mJy up to 4.0Jy. We show that the calibration is linear over that range with respect to target flux and background level. The calibration is based on observations made using 3s exposures; a preliminary analysis shows that the calibration factor may be 1% and 2% lower for 10 and 30s exposures, respectively. We also demonstrate that the calibration is very stable: over the course of the mission, repeated measurements of our routine calibrator, HD 159330, show a rms scatter of only 0.4%. Finally, we show that the point-spread function (PSF) is well measured and allows us to calibrate extended sources accurately; Infrared Astronomy Satellite (IRAS) and MIPS measurements of a sample of nearby galaxies are identical within the uncertainties.