In Web Service Composition (WSC) area, services selection aims at selecting an appropriate candidate from a set of functionally-equivalent services to execute the function of each task in an abstract WSC according to their different QoS values. In despite of many related works, few of previous studies consider transactional constraints in QoS-aware WSC, which guarantee reliable execution of Composite Web Service (CWS) that is composed by a number of unpredictable web services. In this paper, we propose a novel global selection-optimal approach in WSC by considering both transactional constraints and end-to-end QoS constraints. With this approach, we firstly identify building rules and the reduction method to build layer-based Directed Acyclic Graph (DAG) model which can model transactional relationships among candidate services. As such, the problem of solving global optimal QoS utility with transactional constraints in WSC can be regarded as a problem of solving single-source shortest path in DAG. After that, we present Graph-building algorithms and an optimal selection algorithm to explain the specific execution procedures. Finally, comprehensive experiments are conducted based on a real-world web service QoS dataset. The experimental results show that our approach has better performance over other competing selection approaches on success ratio and efficiency.