WASHINGTON—The Trump administration has given a final green light to the controversial Dakota Access Pipeline, according to a court filing issued Tuesday, fulfilling a campaign pledge to boost energy projects but infuriating activists fighting the project.

The U.S. Army Corps of Engineers, an agency of the Department of the Army, said in court filings that the department was planning to issue an outstanding easement under a river in North Dakota that was holding up construction of the oil pipeline. The department also notified...