Algorithms play a crucial role in many technological systems that control or affect various aspects of our lives. As a result, providing explanations for their decisions to address the needs of users and organisations is increasingly expected by laws, regulations, codes of conduct, and the public. However, as laws and regulations do not prescribe how to meet such expectations, organisations are often left to devise their own approaches to explainability, inevitably increasing the cost of compliance and good governance. Hence, we envision Explainability-by-Design, a holistic methodology characterised by proactive measures to include explanation capability in the design of decision-making systems. The methodology consists of three phases: (A) Explanation Requirement Analysis, (B) Explanation Technical Design, and (C) Explanation Validation. This paper describes phase (B), a technical workflow to implement explanation capability from requirements elicited by domain experts for a specific application context. Outputs of this phase are a set of configurations, allowing a reusable explanation service to exploit logs provided by the target application to create provenance traces of the application's decisions. The provenance then can be queried to extract relevant data points, which can be used in explanation plans to construct explanations personalised to their consumers. Following the workflow, organisations can design their decision-making systems to produce explanations that meet the specified requirements. To facilitate the process, we present a software architecture with reusable components to incorporate the resulting explanation capability into an application. Finally, we applied the workflow to two application scenarios and measured the associated development costs. It was shown that the approach is tractable in terms of development time, which can be as low as two hours per sentence.