We have detected and characterized traveling ionospheric disturbances (TIDs) in the mid-latitude ionosphere over the European region using Kharkiv incoherent scatter (IS) radar data acquired near solstices and equinoxes during solar cycle 24 and under magnetically quiet conditions. We analyzed the diurnal, seasonal and solar activity dependence of both large-scale (LS) and medium-scale (MS) TIDs. We studied 140 TID events and estimated their energetic (relative amplitudes), temporal (dominant periods, frequency of occurrence), and spatial (heights of maximum relative amplitudes, vertical and horizontal phase velocities and wavelengths) characteristics. We suggest that the most probable generation mechanisms of magnetically quiet LS and MS TIDs are solar terminators passages, enhanced gravity wave activity and dissipation, severe tropospheric convection, coupling processes between Es layer and F region, polarization electric fields, and Perkins’s instability. We have shown a positive correlation between the heights of the maximum relative TID amplitudes and the solar activity for LSTIDs. The TID characteristics obtained during extremely quiet conditions provide a useful context for analysing the possible TID response to localized energy releases including those of anthropogenic origin, and enable improvements in global and regional ionospheric models by clarifying the contribution of wave processes to the overall energy budget of the atmosphere and ionosphere.