WASHINGTON --A general installed just last month as the Army's top officer is President Barack Obama's surprise choice to become the next chairman of the Joint Chiefs of Staff, two people familiar with the selection process said Wednesday. Gen. Martin Dempsey, an accomplished veteran of the Iraq war, would succeed Navy Adm. Mike Mullen as the president's top military adviser when Mullen's term as chairman ends Sept. 30. Dempsey would have to be confirmed by the Senate. Two people familiar with the choice, who spoke on condition of anonymity because it has not been announced by the White House, said it is scheduled to be made public on Tuesday. Dempsey is a surprise choice because he just began a four-year term as Army chief of staff on April 11. Marine Gen. James Cartwright had long been rumored to be Obama's favorite as the next Joint Chiefs chairman. But Obama informed Cartwright over the weekend that he was no longer a candidate, a defense official said on Wednesday. The official spoke on condition of anonymity in order to discuss internal deliberations. It is not unusual for a service chief like Dempsey to be promoted to chairman of the Joint Chiefs, but rarely, if ever, has one been elevated so quickly. Mullen was selected after serving as the Navy's chief for a little over two years. Cartwright, the current vice chairman of the Joint Chiefs, has been a close adviser to the president, routinely shuttling back and forth to the White House, often as a stand-in when Mullen was traveling. Mullen's term began in 2007 under President George W. Bush, and Obama nominated him for a second two-year term in 2009. Cartwright's chances were hurt by private criticism of his management style and the public release of a Pentagon investigation into claims of misconduct with a young female aide. The Pentagon's inspector general cleared Cartwright of the most serious claims, which suggested he'd had an improper relationship with the woman. But the investigation found that he mishandled an incident in which the aide was drunk and either passed out or fell asleep in his hotel room, where he was working, as his security personnel stood nearby. Army Gen. Ray Odierno is said to be a top candidate to replace Demspey as Army chief. Odierno is currently commander of U.S. Joint Forces Command, which is being dismantled in a Pentagon reorganization. Dempsey fits the bill as among the most battle-tested of today's four-star generals, with two tours of duty in Iraq and a stint as acting commander of Central Command, which covers most of Central Asia and the Middle East. Not well known publicly, he has a reputation inside the Army for forthrightness and innovative thinking. Choosing a successor to Mullen is the latest in a string of changes at the top of Obama's national security team. He recently nominated CIA Director Leon Panetta to succeed Robert Gates as defense secretary this summer, and he picked Army Gen. David Petraeus, the top U.S. commander in Afghanistan, to succeed Panetta at the CIA. The Petraeus and Panetta moves also are subject to confirmation by the Senate. By law, the chairman of the Joint Chiefs is the senior military adviser to the president and the defense secretary but does not command any troops. As its top officer, the chairman serves as the public face of the military and frequently interacts with foreign military leaders. Most chairmen serve two terms of two years each, although Gates in 2007 decided not to recommend a second term for Gen. Peter Pace, who was the first Marine to be chairman. The last Army general to hold the chairman's post was Hugh Shelton, from 1997-2001. Dempsey commanded the 1st Armored Division in Iraq in 2003-04 and later was in charge of U.S. training of Iraqi security forces. He later was tapped to take over U.S. Army Europe, but that changed abruptly in early 2008 when Navy Adm. William J. Fallon stepped down as commander of Central Command and Gates asked Dempsey to temporarily take on that job. At the time, Dempsey was deputy commander under Fallon. In December 2008, he moved on to head U.S. Army Training and Doctrine Command and served there until early this year. In that job, he was responsible for steering the Army's thinking on how to fight wars, large and small. Dan Goure, a military analyst at the Lexington Institute, applauded the Dempsey selection. "He has both field experience and experience in defining strategy and doctrine for the military," Goure said. "He is an extraordinarily well respected Army leader, and in particular this puts the Army now in critical positions for continuing the war on terror, with David Petraeus at CIA and Marty Dempsey now as chairman." On the day he become Army chief of staff, Dempsey wrote in a brief note to all soldiers that while the Army and other branches of the military are likely to face declining budgets, the Army must never skimp on three qualities: trust, discipline and fitness. "These qualities have to exist in every unit and in every soldier of our Army all the time," he wrote. "When I come to visit your organization ... I'll want to know what you're doing to develop a climate of trust, to ensure the discipline of your soldiers, and to increase the fitness of the force." With Cartwright's term as vice chairman ending in August, Obama also is preparing to select his successor. Among those mentioned most prominently is the current Air Force chief of staff, Gen. Norton Schwartz. Schwartz took over the Air Force three years ago when Gates sacked the service's top civilian and uniformed leaders in a dustup over a series of nuclear-related mishaps. Since then, Schwartz has been credited with quietly restoring proper oversight of the mission and rebuilding Gates' confidence in the Air Force.