In volume visualization, users can interactively explore the three-dimensional data by specifying color and opacity mappings in the transfer function (TF) or adjusting lighting parameters, facilitating meaningful interpretation of the underlying structure. However, rendering large-scale volumes demands powerful GPUs and high-speed memory access for real-time performance. While existing novel view synthesis (NVS) methods offer faster rendering speeds with lower hardware requirements, the visible parts of a reconstructed scene are fixed and constrained by preset TF settings, significantly limiting user exploration. This paper introduces inverse volume rendering via Gaussian splatting (iVR-GS), an innovative NVS method that reduces the rendering cost while enabling scene editing for interactive volume exploration. Specifically, we compose multiple iVR-GS models associated with basic TFs covering disjoint visible parts to make the entire volumetric scene visible. Each basic model contains a collection of 3D editable Gaussians, where each Gaussian is a 3D spatial point that supports real-time scene rendering and editing. We demonstrate the superior reconstruction quality and composability of iVR-GS against other NVS solutions (Plenoxels, CCNeRF, and base 3DGS) on various volume datasets. The code is available at https://github.com/TouKaienn/iVR-GS.