An emerging IT delivery model, Cloud Computing, can significantly reduce IT costs and complexities while improving workload optimisation and service delivery. More and more organisations are planning to migrate their existing systems into this internet-driven computing environment. This investigation is proposed for this purpose and will be undertaken with two main aims. The first aim is to establish a general framework and method to assist with the evolution of legacy systems into and within the Cloud environment. The second aim is to evaluate the proposed approach and demonstrate that such an approach can be more effective than developing Cloud services from scratch. The underlying research procedure of this thesis consists of observation, proposition, test and conclusion. This thesis contributes a novel evolution approach in Cloud computing. A technical solution framework is proposed through a three-dimensional software evolution paradigm, which can cover the relationships of software models, software functions and software qualities in different Cloud paradigms. Finally, the evolved service will be run in the Cloud environments. The approach framework is implemented by three phases: 1) legacy system analysis and extraction, which proposes an analysis approach to decide the legacy system in the Cloud environment and to adopt the techniques of program slicing with improved algorithm and software clustering for extracting legacy components. 2) Cloud-oriented service migration including evolving software into and within Cloud. The process of evolving software 'INTO' Cloud can be viewed mainly as changing software qualities on software models. The process of evolving software 'WITHIN' Cloud can be viewed mainly as changing software functions on software models, the techniques of program and model transformation and software architecture engineering are applied. 3) Cloud service integration, which integrates and deploys the service in the Cloud environment. The proposed approach is proved to be flexible and practical by the selected case study. Conclusions based on analysis and future research are discussed at the end of the thesis.