Although recent generative image compression methods have demonstrated impressive potential in optimizing the rate-distortion-perception trade-off, they still face the critical challenge of flexible rate adaptation to diverse compression necessities and scenarios. To overcome this challenge, this paper proposes a $\textbf{Control}$lable $\textbf{G}$enerative $\textbf{I}$mage $\textbf{C}$ompression framework, $\textbf{Control-GIC}$, the first capable of fine-grained bitrate adaptation across a broad spectrum while ensuring high-fidelity and generality compression. We base Control-GIC on a VQGAN framework representing an image as a sequence of variable-length codes ($\textit{i.e.}$ VQ-indices), which can be losslessly compressed and exhibits a direct positive correlation with bitrates. Drawing inspiration from the classical coding principle, we correlate the information density of local image patches with their granular representations. Hence, we can flexibly determine a proper allocation of granularity for the patches to achieve dynamic adjustment for VQ-indices, resulting in desirable compression rates. We further develop a probabilistic conditional decoder capable of retrieving historic encoded multi-granularity representations according to transmitted codes, and then reconstruct hierarchical granular features in the formalization of conditional probability, enabling more informative aggregation to improve reconstruction realism. Our experiments show that Control-GIC allows highly flexible and controllable bitrate adaptation where the results demonstrate its superior performance over recent state-of-the-art methods.