Milley assumed command of Fort Hood on December 20, 2012, succeeding Lt. Gen. Don M. Campbell, Jr. who left to command U.S. Army Europe and the Seventh Army in Germany.
Dunford's spokesman, Col. Patrick Ryder, said all indications are that Dunford will serve his full term.
Trump's announcement comes months earlier than expected.
President Donald Trump said he'll be making an announcement on Saturday concerning the Joint Chiefs of Staff.
But he opted to announce the news on Twitter before heading to the game.
The chairman is the highest-ranking military officer in the country and serves as the principal military adviser to the President.
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.
Luis Valbuena, Jose Castillo's deaths may have been criminal act, reports say
Valbuena, 33, and Castillo, 37, were playing in a Venezuelan winter baseball league and were teammates on the Cardenales de Lara. Castillo played for the Pittsburgh Pirates, San Francisco Giants and the Houston Astros between 2004 and 2008.
Milley made the early decision to charge Bergdahl with desertion and misbehavior before the enemy. Trump also will pick a replacement for Milley as Army chief.
Milley's holds a Bachelor's Degree in Political Science from Princeton University, a Master's Degrees from Columbia University (International Relations) and from the U.S. Naval War College (National Security and Strategic Studies).
Mr. Trump re-nominated him in 2017 for a second term.
Dunford was nominated to the post in 2015 by former US President Barack Obama.
He says: "I can give you a little hint: It will have to do with the Joint Chiefs of Staff and succession".
The Trump family may also have an affinity for the Army.
Some officials said privately that they expected Goldfein to be chosen because the Air Force was due to receive the chairmanship - two Marine generals, an Army general and a Navy admiral have served since the Air Force's last chairman left office in 2005.