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The Dark Energy Spectroscopic Instrument (DESI) is a 5000 fiber multi-object spectrometer now being installed at the prime focus of the 4 m Mayall telescope at Kitt Peak. Using DESI to measure ∼35 million galaxy redshifts and using the Baryon Acoustic Oscillation (BAO) technique to measure distances, the results will probe the nature of the recently discovered mysterious component of our universe called dark energy. Computer controlled robotic positioners move the 120 μm diameter fibers to positions of galaxies whose location on the sky have been obtained in a previous target selection imaging survey. To achieve good throughput the fibers should be centered on the target position to within 3 μm. The robotic positioners however are only capable of a 50 μm precision on their first move. To achieve the desired precision, the Fiber View Camera (FVC) system has been implemented. The FVC, located near the hole in the primary mirror of the Mayall telescope, has been designed to take an exposure of the focal plane, located at the prime focus some 12 m above the FVC, after the robotic positioners have completed their first move. The FVC is intended to measure the fiber locations with a precision of 3 μm and issue a set of fiber coordinate corrections for the second move correcting the fiber positions by the robotic positioners. Tests show that after two iterations better than 99% of the fibers will be in their intended location to within the desired precision. This paper describes the design of the FVC system, the R&D program preceding the final design, and the tests that have been carried out to demonstrate that the FVC can achieve the required precision. [ABSTRACT FROM AUTHOR]