One major challenge for autonomous attitude takeover control for on-orbit servicing of spacecrafts is that an accurate dynamic motion model of the combined vehicles is highly nonlinear, complex, and often costly to identify online, which makes traditional model-based control impractical for this task. To address this issue, a recursive online sparse Gaussian process (GP)-based learning strategy for attitude takeover control of non-cooperative targets with maneuverability is proposed, where the unknown dynamics are online compensated based on the learnt GP model in a semi-feedforward manner. The method enables the continuous use of on-orbit data to successively improve the learnt model during online operation and has reduced computational load compared to standard GP regression. Next to the GP-based feedforward, a feedback controller is proposed that varies its gains based on the predicted model confidence, ensuring robustness of the overall scheme. Moreover, rigorous theoretical proofs of Lyapunov stability and boundedness guarantees of the proposed method-driven closed-loop system are provided in the probabilistic sense. A simulation study based on a high-fidelity simulator is used to show the effectiveness of the proposed strategy and demonstrate its high performance.