Herein, we propose novel, highly effective Pt-free counter electrode (CE) material for dye-sensitized solar cells (DSSC) based on the hierarchical carbon nanofibers/carbon nanotubes/NiCo (eCNF/CNT/NiCoNP) ternary nanocomposites. The materials were obtained by combining the electrospinning technique and CCVD synthesis of carbon nanotubes directly on the surface of eCNF. By using various conditions of the CNT growth, it was possible to obtain series of nanocomposites differing with their morphology, surface chemistry, and structural ordering. The conducted studies unraveled significant correlations between the disordering of the nanocomposites, and their electrocatalytic activity towards reduction of I3−. The investigation methods included i.a. SEM, TEM, XPS, UPS, EDS, XRD, SAED, CV, EIS and J-V characterizations. The counter electrodes based on the nanocomposite synthetized at the lowest CCVD temperature of 700 °C exhibited remarkable catalytical activity as evidenced by very low charge transfer resistance of 0.93 Ω cm2. Based on the obtained data, we propose new, alternative interpretation of the additional minor arc appearing at the high-frequency region of EIS Nyquist spectra of carbon based-CE. The DSSC with eCNF/CNT/NiCoNP-electrodes were characterized by efficiencies up to 7.08% (avg. η = 6.95%), which was higher than for Pt-based devices (avg. η = 6.80%), thus demonstrating excellent performance of prepared CE. Our results confirm that the eCNF/CNT/NiCoNP nanocomposite material is a promising low-cost CE alternative for DSSC.