Enterprises are organisations with multiple business processes; they often use Enterprise Information Systems (EIS) to support these business processes. The concept of an EIS has arisen from the need to deal with the increasingly volatile requirements of modern large{scale organisations. EIS are growing in use and are now being used to support government, health care, and non-profit / non-governmental organisations. The development of EIS has been affected significantly by the complexity and size of enterprises and their business processes, in addition to the influences of economical, social, and governmental factors. There are many challenges associated with building EIS. Three critical ones identied in the literature are: adequately satisfying organisational requirements; building valid and stakeholder-acceptable business processes; and providing repeatable and rigorous approaches to establish shared understanding of EIS goals. These challenges are difficult to cope with because of the need to deal with different goals, changes in goals, and the problem of how to transform these goals into system requirements and, ultimately, to an EIS architecture. This thesis contributes a rigorous approach for identifying and describing the enterprise-level requirements of IT developers, managers, and other stakeholders of an enterprise. The approach provides two modelling and tool-supported processes to help establish a rigorous model of EIS goals. It also provides support for transforming goals to a strategic EIS architecture. The approach presented in the thesis is based on the concepts of Goal-oriented software engineering. The thesis presents a novel Process Model, KAOS-B that extends goal-oriented software engineering approaches with new concepts and techniques for EIS. Further, to support the transition from requirements to an EIS architecture, an EIS Architecture Process Model (EAPM), is designed and evaluated. Using KAOS-B and EAPM in concert provides a rigorous, repeatable and tool-supported approach for analysing, and designing a strategic EIS architecture. The thesis illustrates the approach with two substantial examples from the health informatics and critical systems domain.