We present new spectroscopic observations of the stellar cluster population of region B in the prototype starburst galaxy M82 obtained with the Gemini North 8.1 m telescope. By coupling the spectroscopy with UBVI photometry acquired with the Advanced Camera for Surveys (ACS) on the Hubble Space Telescope (HST), we derive ages, extinctions, and radial velocities for seven young massive clusters (YMCs) in region B. We find the clusters to have ages between 80 and 200 Myr and velocities in the range 230-350 km s super(-1), while the extinctions Av vary between similar to 1 and 2.5 mag. We also find evidence of differential extinction across the faces of some clusters, which hinders the photometric determination of ages and extinctions in these cases. The cluster radial velocities indicate that the clusters are located at different depths within the disk and are on regular disk orbits. Our results overall contradict the findings of previous studies, in which region B was thought to be a bound region populated by intermediate-age clusters that formed in an independent, offset starburst episode that commenced 600 Myr-1 Gyr ago. Our findings instead suggest that region B is optically bright because of low-extinction patches, and that this allows us to view the cluster population of the inner M82 disk, which probably formed as a result of the last encounter with M81. This study forms part of a series of papers whose aim is to study the cluster population of M82 using deep optical spectroscopy and multiband photometry.