Background: Despite the emergence of app evaluation tools, there remains no well-defined process receptive to diverse local needs, rigorous standards, and current content. The need for such a process to assist in the implementation of app evaluation across all medical fields is evident. Such a process has the potential to increase stakeholder engagement and catalyze interest and engagement with present-day app evaluation models. Objective: This study aimed to develop and pilot test the Technology Evaluation and Assessment Criteria for Health apps (TEACH-apps). Methods: Tailoring a well-known implementation framework, Replicating Effective Programs, we present a new process to approach the challenges faced in implementing app evaluation tools today. As a culmination of our experience implementing this process and feedback from stakeholders, we present the four-part process to aid the implementation of mobile health technology. This paper outlines the theory, evidence, and initial versions of the process. Results: The TEACH-apps process is designed to be broadly usable and widely applicable across all fields of health. The process comprises four parts: (1) preconditions (eg, gathering apps and considering local needs), (2) preimplementation (eg, customizing criteria and offering digital skills training), (3) implementation (eg, evaluating apps and creating educational handouts), and (4) maintenance and evolution (eg, repeating the process every 90 days and updating content). TEACH-apps has been tested internally at our hospital, and there is growing interest in partnering health care facilities to test the system at their sites. Conclusions: This implementation framework introduces a process that equips stakeholders, clinicians, and users with the foundational tools to make informed decisions around app use and increase app evaluation engagement. The application of this process may lead to the selection of more culturally appropriate and clinically relevant tools in health care. [J Med Internet Res 2020;22(8):e18346]