Gaussian Splatting techniques have recently enabled high-quality 3D scene reconstruction and real-time novel view synthesis. These approaches, however, are limited by the pinhole camera model and lacks support for modeling and rendering defocus effects. Departing from this, we introduce DOF-GS --- a new framework that aussian Splatting with a finite-aperture camera model and explicit, differentiable defocus rendering, enabling it to function as a post-capture control tool. DOF-GS enables dynamic depth-of-field (DOF) adjustment through on-demand post-capture aperture and focal distance control for the first time, to the best of our knowledge. By using multi-view images with moderate defocus blur as input, our framework learns inherent camera characteristics and reconstruct sharp details of the underlying scene, particularly, enabling rendering with varying DOF effects, post-capture and optimization. Additionally, our framework extracts circle-of-confusion cues during optimization to identify in-focus regions in input views, enhancing the reconstructed 3D scene details. Experimental results demonstrate that DOF-GS supports post-capture refocusing, adjustable defocus and high-quality all-in-focus rendering, from multi-view images with uncalibrated defocus blur.