Cloud computing is the latest computing paradigm that delivers hardware and software resources as virtualized services in which users are free from the burden of worrying about the low-level system administration details. Migrating Web applications to Cloud services and integrating Cloud services into existing computing infrastructures is non-trivial. It leads to new challenges that often require innovation of paradigms and practices at all levels: technical, cultural, legal, regulatory, and social. The key problem in mapping Web applications to virtualized Cloud services is selecting the best and compatible mix of software images (e.g., Web server image) and infrastructure services to ensure that Quality of Service (QoS) targets of an application are achieved. The fact that, when selecting Cloud services, engineers must consider heterogeneous sets of criteria and complex dependencies between infrastructure services and software images, which are impossible to resolve manually, is a critical issue. To overcome these challenges, we present a framework (called CloudGenius) which automates the decision-making process based on a model and factors specifically for Web server migration to the Cloud. CloudGenius leverages a well known multi-criteria decision making technique, called Analytic Hierarchy Process, to automate the selection process based on a model, factors, and QoS parameters related to an application. An example application demonstrates the applicability of the theoretical CloudGenius approach. Moreover, we present an implementation of CloudGenius that has been validated through experiments.