The Dark Energy Spectroscopic Instrument (DESI) is under construction to measure the expansion history of the universe using the Baryon Acoustic Oscillation technique. The spectra of 35 million galaxies and quasars spanning over 14,000 deg2 are measured during the life of the experiment. A prime focus corrector for the Kitt Peak National Observatory Mayall telescope delivers light to 5000 robotically positioned optic fibers. The fibers in turn feed 10 broadband spectrographs. Proper alignment of the focal plate structure, mainly consisting of a focal plate ring and 10 focal plate petals, is crucial in ensuring minimal loss of light in the focal plane. A coordinate measurement machine (CMM) metrology-based approach to alignment requires comprehensive characterization of critical dimensions of the petals and the ring, all of which are 100% inspected. The metrology data not only serve for quality assurance but also, with careful modeling of geometric transformations, inform the initial choice of integration accessories, such as gauge blocks, pads, and shims. The integrated focal plate structure is inspected again on a CMM, and each petal is adjusted individually according to the updated focal plate metrology data until all datums are extremely close to nominal positions and optical throughput nearly reached the theoretically best possible value. We present our metrology and alignment methodology and complete results for 12 official DESI petals. The as-aligned, total RMS optical throughput for 6168 positioner holes of 12 production petals is indirectly measured to be 99.88 % ± 0.12 % , well above the 99.5% project requirement. The successful alignment fully demonstrated the wealth of data, reproducibility, and micron-level precision made available by our CMM metrology-based approach.