The van der Waals (vdW) ferromagnet Fe_3-δ GeTe₂ has garnered significant research interest as a platform for skyrmionic spin configurations, that is, skyrmions and skyrmionic bubbles. However, despite extensive efforts, the origin of the Dzyaloshinskii-Moriya interaction (DMI) in Fe_3-δ GeTe₂ remains elusive, making it challenging to acquire these skyrmionic phases in a controlled manner. In this study, it is demonstrated that the Fe content in Fe_3-δ GeTe₂ has a profound effect on the crystal structure, DMI, and skyrmionic phase. For the first time, a marked increase in Fe atom displacement with decreasing Fe content is observed, transforming the original centrosymmetric crystal structure into a non-centrosymmetric symmetry, leading to a considerable DMI. Additionally, by varying the Fe content and sample thickness, a controllable transition between Néel-type skyrmions and Bloch-type skyrmionic bubbles is achieved, governed by a delicate interplay between dipole-dipole interaction and the DMI. The findings offer novel insights into the variable skyrmionic phases in Fe_3-δ GeTe₂ and provide the impetus for developing vdW ferromagnet-based spintronic devices.