Mountain Valley Pipeline Completion Act This bill establishes requirements to expedite the completion of the Mountain Valley Pipeline, which is a natural gas pipeline located in Virginia and West Virginia. Specifically, the bill ratifies and approves all authorizations, permits, verifications, extensions, biological opinions, incidental take statements, and any other approvals or orders issued pursuant to federal law related to the Mountain Valley Pipeline. In addition, the bill establishes a deadline by which the U.S. Army Corps of Engineers must issue permits or verifications necessary to complete the construction of the pipeline across the waters of the United States and to allow for the operation and maintenance of the pipeline, the Forest Service must amend the Land and Resource Management Plan for the Jefferson National Forest as specified by the bill, and the Department of Interior must grant specified rights-of-way and temporary use permits. Finally, the bill prohibits judicial review of certain approvals related to the pipeline.