We describe the design and commissioning of the photon tagging beamline installed in experimental Hall B at the Thomas Jefferson National Accelerator Facility (JLab). This system can tag photon energies over a range from 20% to 95% of the incident electron energy, and is capable of operation with beam energies up to 6.1 GeV. A single dipole magnet is combined with a hodoscope containing two planar arrays of plastic scintillators to detect energy-degraded electrons from a thin bremsstrahlung radiator. The first layer of 384 partially overlapping small scintillators provides photon energy resolution, while the second layer of 61 larger scintillators provides the timing resolution necessary to form a coincidence with the corresponding nuclear interaction triggered by the tagged photon. The definitions of overlap channels in the first counter plane and of geometric correlation between the two planes are determined using digitized time information from the individual counters. Auxiliary beamline devices are briefly described, and performance results to date under real operating conditions are presented. The entire photon-tagging system has met or exceeded its design goals.