Conceptual design of mechanisms is a crucial part of achieving product innovation as mechanisms perform the transmission and transformation of specific motions in the machine. However, existing approaches for automated synthesis of mechanisms are either inefficient or prone to a loss of optimal solutions. To fill this gap, a systematic online decision-making method using Thompson Sampling (TS) based Monte Carlo Tree Search (MCTS) for automated conceptual design of mechanisms is proposed. The functional transformation relationships between inputs and outputs of the intended mechanism system are used to determine combinatorial patterns. Then, a functional representation model is constructed based on the combination rules of motion features and the inference relationships of function elements to represent a range of primitive mechanisms as fundamental building blocks. Finally, the optimal action selection strategy based on TS is applied into MCTS to develop Dirichlet based Monte Carlo Tree Search (D-MCTS) algorithm for searching mechanism building blocks. In addition, the conceptual design of the beat-up mechanism as well as the stitching and feeding mechanism are conducted to validate the feasibility of the proposed approach. Compared with specialized heuristics, D-MCTS achieves higher efficiency in finding the best combination of mechanism building blocks. Compared with other common algorithms, D-MCTS can always avoid the local optima trap to find the global optimal solution without any necessary hyper-parameter tuning. The proposed method exhibits a more balanced performance in exploration and exploitation, which provides better solutions for mechanism synthesis of given requirements.