Process modelling is a design approach where a system or procedure is decomposed in a number of abstract, independent, but connected processes, and then recomposed into a well-defined workflow specification. Research in formal verification, for its part, and theorem proving in particular, is focused on the rigorous verification of system properties using logical proof. This thesis introduces a systematic methodology for process modelling and composition based on formal verification. Our aim is to augment the numerous benefits of a workflow based specification, such as modularity, separation of concerns, interoperability between heterogeneous (including human-based) components, and optimisation, with the high level of trust provided by formally verified properties, such as type correctness, systematic resource accounting (including exception handling), and deadlock-freedom. More specifically, we focus on bridging the gap between the deeply theoretical proofs-as-processes paradigm and the highly pragmatic tasks of process specification and composition. To accomplish this, we embed the proofs-as-processes paradigm within the modern proof assistant HOL Light. This allows the formal, mechanical translation of Classical Linear Logic (CLL) proofs to p-calculus processes. Our methodology then relies on the specification of abstract processes in CLL terms and their composition using CLL inference. A fully diagrammatic interface is used to guide our developed set of high level, semi-automated reasoning tools, and to perform intuitive composition actions including sequential, parallel, and conditional composition. The end result is a p-calculus specification of the constructed workflow, with guarantees of correctness for the aforementioned properties. We can then apply a visual, step-by-step simulation of this workflow or perform an automated workflow deployment as executable code in the programming language Scala. We apply our methodology to a use-case of a holiday booking web agent and to the modelling of real-world collaboration patterns in healthcare, thus demonstrating the capabilities of our framework and its potential use in a variety of scenarios.