Final answer:
The written agreement in question is a Project Charter, which serves as a formal document that authorizes a project's start and outlines its key details.
Step-by-step explanation:
The written agreement between the Project Manager (PM), senior management, and the functional managers, who are committing resources and/or people to the project, is known as a Project Charter. This document outlines the objectives, scope, and participants in a project. Its purpose is to establish a common understanding among stakeholders and to authorize the commencement of the project.