Dynamic execution of a business process requires the selection and composition of multiple existing services regardless of their locations, platforms, execution speeds, etc. Thus web service selection appears as a challenging and elusive task especially when the service task has to be executed based on user requirements at the runtime. This paper presents our Semantic-Based Business Process Execution Engine (SBPEE) for the dynamic execution of business processes by the orchestration of various exposed web services. SBPEE is based on our designed Project Domain Ontology (PrjOnt) that captures user specifications and SWRL rules which classify the user specification into a specific category according to the business logic and requirements of an enterprise. Based on this classification of the user project and requirements, our semantic engine selects web services from the service repository for the dynamic execution of a business process. SBPEE matches functional requirements of a web service and required QoS attributes to identify the list of pertinent candidate services to fulfil the complex business process transactions. Finally, we present our case study on Create Order business process that aims at creating an order for the customer by following various web services for its task completion.