We conducted a deep spectroscopic survey, named SSA22-HIT, in the SSA22 field with the DEep Imaging MultiObject Spectrograph (DEIMOS) on the Keck telescope, designed to tomographically map high-z H i gas through analysis of Ly{alpha} absorption in background galaxies spectra. In total, 198 galaxies were spectroscopically confirmed at 2.5<z<6 with a few low-z exceptions in the 26x15arcmin^2^ area, of which 148 were newly determined in this study. Our redshift measurements were merged with previously confirmed redshifts available in the 34x27arcmin^2^ area of the SSA22 field. This compiled catalog containing 730 galaxies of various types at z>2 is useful for various applications, and it is made publicly available. Our SSA22-HIT survey has increased by approximately twice the number of spectroscopic redshifts of sources at z>3.2 in the observed field. From a comparison with publicly available redshift catalogs, we show that our compiled redshift catalog in the SSA22 field is comparable to those among major extragalactic survey fields in terms of a combination of wide area and high surface number density of objects at z>2. About 40% of the spectroscopically confirmed objects in SSA22-HIT show reasonable quality of spectra in the wavelengths shorter than Ly{alpha} when a sufficient amount of smoothing is adopted. Our data set enables us to make the HI tomographic map at z>~3, which we present in a parallel study.