We propose a machine learning-driven optimisation framework for analog circuit design in this paper. The primary objective is to determine the device sizes for the optimal performance of analog circuits for a given set of specifications. Our methodology entails employing machine learning models and spice simulations to direct the optimisation algorithm towards achieving the optimal design for analog circuits. Machine learning based global offline surrogate models, with the circuit design parameters as the input, are built in the design space for the analog circuits under study and is used to guide the optimisation algorithm, resulting in faster convergence and a reduced number of spice simulations. Multi-layer perceptron and random forest regressors are employed to predict the required design specifications of the analog circuit. Since the saturation condition of transistors is vital in the proper working of analog circuits, multi-layer perceptron classifiers are used to predict the saturation condition of each transistor in the circuit. The feasibility of the candidate solutions is verified using machine learning models before invoking spice simulations. We validate the proposed framework using three circuit topologies--a bandgap reference, a folded cascode operational amplifier, and a two-stage operational amplifier. The simulation results show better optimum values and lower standard deviations for fitness functions after convergence. Incorporating the machine learning-based predictions proposed in the optimisation method has resulted in the reduction of spice calls by 56%, 59%, and 83% when compared with standard approaches in the three test cases considered in the study.