Skyrmions are nontrivial spiral spin textures considered as potential building blocks for ultrafast and power efficient spintronic memory and logic devices. Controlling their chirality would provide an additional degree of freedom and enable new functionalities in these devices. Achieving such control requires adjusting the interfacial Dzyaloshinskii-Moriya interaction (DMI). Thanks to Brillouin Light scattering measurements in Ta/FeCoB/TaOx trilayer, we have evidenced a DMI sign crossover when tuning TaOx oxidation and suspected another DMI sign crossover when tuning FeCoB thickness. Moreover, using polar magneto-optical Kerr effect microscopy, we demonstrate skyrmion chirality inversion through their opposite current induced motion direction either by changing FeCoB thickness or TaOx oxidation rate. This chirality inversion enables a more versatile manipulation of skyrmions, paving the way towards multidirectional devices.