A new experimental system was recently developed to measure the mobility of both positive and negative ions: the Dual-Polarity Ion Drift Chamber (DP-IDC). In this work, we present a detailed description of the experimental setup and technique used, as well as the initial studies carried out. The reduced ion mobilities of SF5− and SF6− were measured in pure SF6, SF6-CF4 and SF6-N2, for pressures between 10 and 30 Torr and reduced electric fields ranging from 10 to 40 Td. The results were compared with experimental and theoretical data available, and a good performance was found. The study of the mobility of positive ions in Ne-CF4 gas mixtures was also performed, with the results obtained showing a good agreement with those determined in a similar setup previously developed by our group. The importance of this type of studies is also discussed, along with the future prospects for this experimental system.