Dempsey currently is the deputy commander of U.S. Central Command and previously served two tours in Iraq as a senior commander. His nomination is subject to Senate confirmation.
Dempsey would replace Gen. David McKiernan in Europe. In announcing Dempsey's selection the Pentagon did not say when he would take over, but it is expected to happen in May or June. McKiernan has been selected as the next commander of NATO forces in Afghanistan.
Odierno, currently commander of the Army's Third Corps, based at Fort Hood, Texas, has been the top day-to-day commander in Iraq under Gen. David Petraeus for the past 15 months. He is due to depart Iraq this month as the Army's 18th Airborne Corps takes over as Petraeus' main command.
Odierno has been nominated for a fourth star, subject to Senate confirmation, and would take over for Cody this summer.
In his new Pentagon assignment Odierno would work under Gen. George Casey, who preceded Petraeus as the top commander in Iraq. Odierno previously commanded the 4th Infantry Division in Iraq from March 2003 to April 2004; his soldiers were credited with capturing Saddam Hussein in December 2003.
Cody, 57, is expected to retire after an Army career that began in June 1972 with graduation from West Point. After a wide range of assignments he became Army vice chief of staff in June 2004, replacing Casey.
Cody was the first career aviator to be elevated to the vice chief of staff job. Years earlier, he had made a mark in Army history from the cockpit of the Apache helicopter.
He was piloting one of eight Apaches that sneaked into Iraqi airspace on the night of Jan. 17, 1991, and attacked crucial air defense radar sites with Hellfire missiles and 30mm gunfire, clearing a path for fighters and bombers that launched the first U.S. war against Iraq.
The Persian Gulf War's top commander, Army Gen. Norman Schwarzkopf, said later they had "plucked out the eyes" of Iraq's air defenses, and Cody won a Distinguished Flying Cross for his exploits.