We propose a novel framework to enable Knowledge Graphs (KGs) sharing while ensuring that information that should remain private is not directly released nor indirectly exposed via derived knowledge, maintaining at the same time the embedded knowledge of the KGs to support business downstream tasks. Our approach produces a privacy-preserving KG as an augmentation of the input one via controlled addition of nodes and edges as well as re-labeling of nodes and perturbation of weights. We introduce a novel privacy measure for KGs, which considers derived knowledge, a new utility metric that captures the business semantics we want to preserve, and propose two novel anonymisation algorithms. Our extensive experimental evaluation, with both synthetic graphs and real-world datasets, confirms the effectiveness of our approach.