Final answer:
The document that formally initiates a project and outlines its objectives and management is the project charter. It is crucial for defining the project's scope, direction, and governance, and for authorizing the project manager to use organizational resources.
Step-by-step explanation:
The document that formally recognizes the existence of a project and provides direction on the project's objectives and management is known as a project charter. The project charter is a critical document in project management, as it defines the scope, objectives, and overall direction for the project. It also outlines the roles and responsibilities of the project team, sets forth the resources and budget, and establishes the project's governance framework.
While a business case presents the justification for initiating a project, including the benefits and costs, the stakeholder register is a document that lists all the stakeholders and their information, and the stakeholder management strategy outlines the approach for engaging stakeholders throughout the project. However, it is the project charter that officially starts the project and gives the project manager the authority to allocate organizational resources to project activities.