Probabilistic registration algorithms [e.g., coherent point drift, (CPD)] provide effective solutions for point cloud alignment. However, using the original CPD algorithm for automatic registration of terrestrial laser scanner (TLS) point clouds is highly challenging because of density variations caused by scanning acquisition geometry. In this letter, we propose a new global registration method, introducing the use of the CPD framework for TLS point clouds. We first consider the measurement geometry and the intrinsic characteristics of the scene to simplify points. In addition to the Euclidean distance, we incorporate geometric information as well as structural constraints in the probabilistic model to optimize the so-called matching probability matrix. Among the structural constraints, we use a spectral graph to measure the structural similarity between matches at each iteration. The method is tested on three data sets collected by different TLS scanners. Experimental results demonstrate that the proposed method is robust to density variations and can decrease iterations effectively. The average registration errors of the three data sets are 0.05, 0.12, and 0.08 m, respectively. It is also shown that our registration framework is superior to the state-of-the-art methods in terms of both registration errors and efficiency. The experiments demonstrate the effectiveness and efficiency of the proposed probabilistic global registration.