If confirmed, Dunford, 59, will replace Army Gen. Martin Dempsey to become the 19th chairman. Dempsey is expected to retire in October when his second term expires.
Obama called Dunford "one of the most admired officers in our military."
"I have been extraordinarily impressed by Joe -- from the Situation Room, where he helped to shape our enduring commitment to Afghanistan, to my visit last year to Bagram, where I saw his leadership firsthand," Obama said.
"I know Joe. I trust him. He's already proven his ability to give me his unvarnished military advice based on his experience on the ground. Under his steady hand, we've achieved key milestones, including the transition to Afghan responsibility for security, historic Afghan elections, and the drawdown of U.S. forces -- setting the stage for our combat mission there."
Dunford became commandant in October. Prior to that he led all U.S. and NATO forces in Afghanistan between February 2013 and August 2014. Should he be confirmed, he would be the most senior officer and adviser to the president.
U.S. Sen. Jack Reed, D-R.I., a member of the Senate Armed Services Committee, said he supported the decision.
"I have come to greatly value General Dunford's counsel and insight, and I particularly appreciate the concern he has for our men and women in uniform under his command," he said.
Obama also announced his nomination of Air Force Gen. Paul Selva as the vice chairman to replace outgoing Admiral Sandy Winnefeld.
Selva has 35 years of military service and was a leader of Air Mobility Command.
"Paul also served as Secretary of State Clinton's military advisor for the first years of my presidency, so he grasps the strategic environment in which our forces operate," Obama said. "He understands that our military, as powerful as it is, is one tool that must be used in concert with all the elements of our national power."