The officials confirmed the decision Friday on condition of anonymity because it had not been announced.
But he opted to announce the news on Twitter before heading to the game.
Mattis and Dunford are expected to attend the Army-Navy game on Saturday along with Trump.
Pentagon spokesman Lt. Col. Mike Andrews said, "We are aware of the President's nomination and share his confidence" in Milley to be the Joint Chiefs chairman. Milley started the first U.S. Army-Navy ice hockey game in 2016 in advance of the 2016 Army-Navy football game. Dunford has been serving as chairman since 2015.
Milley is known as a charismatic, outgoing leader who has not been afraid to offer candid and sometimes blunt assessments to Congress.
Trump chief of staff John Kelly to leave White House job
Earlier on Saturday, he announced army General Mark Milley as his pick to be the new chairman of the joint chiefs of staff. I have to wonder if the President isn't seriously considering just leaving the job vacant and running the circus himself.
The chairman of the House Armed Services Committee praised Milley for his "direct, insightful military assessments based upon his intellect and years of experience". He has served in numerous command and leadership position, including in Iraq and Afghanistan. More recently, he has worked with his senior officers to reverse a shortfall in Army recruiting when the service fell far short of its annual goal this year.
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. Milley made the decision to charge Bergdahl in 2015 with desertion and misbehavior before the enemy, for which Bergdahl ultimately received a dishonorable discharge but avoided prison time.
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). Trump nominated him for a second two-year term last year.
Previous chairmen served two two-year terms if they were re-nominated.