Milley will be the first Chairman of the Joint Chiefs of Staff to serve a single 4-year term. In a 2015 visit to the school, he stressed the importance of serving others.
In addition to the scheduled change of the chairman, several other key slots on the Joint Chiefs of Staff are scheduled to open next year.
Under the law, the chairman of the Joint Chiefs of Staff is the highest-ranking and senior-most military officer in the U.S. Armed Forces and is the principal military advisor to the president.
Milley's nomination will need to be confirmed by the Senate. Before that he had served as Commandant of the Marine Corps.
"I have another one for tomorrow that I'm going to be announcing at the Army-Navy game", Trump said, according to a White House pool report.
He commanded the 1st Battalion, 506th Infantry, 2nd Infantry Division; the 2nd Brigade, 10th Mountain Division; served as the Deputy Commanding General for the 101st Airborne (Air Assault); and served as the Commanding General for 10th Mountain Division.More news: Marine Planes Crash Off Japan Coast, Search and Rescue Underway
Trump hinted earlier on Friday that he would be announcing new military leadership on Saturday when he attends the Army-Navy football game.
Milley served as a Green Beret and commanded troops in Afghanistan.
As the Army's top leader, he helped shepherd the groundbreaking move of women into front-line infantry and other combat positions, while warning that it would take time to do it right. Bergdahl was eventually found guilty, reduced in rank to private, dishonorably discharged and fined $10,000, but was spared any additional prison time. He has been Army chief of staff since 2015.
A native of Massachusetts, Milley holds degrees from Princeton University and Columbia University. Trump nominated him for a second two-year term last year.
Inside the Pentagon, Milley was seen as one of two top choices to succeed Dunford alongside the Air Force's top officer, Gen. David Goldfein, a veteran fighter pilot who has served as chief of staff of his service since 2016.