(Adds Bush accepting nominations) WASHINGTON, Jan 5 (Reuters) - President George W. Bush chose two new commanders on Friday to lead U.S. military efforts in Iraq as he prepares to revamp his war strategy. Bush picked Army Lt. Gen. David Petraeus, highly regarded within the military, as the top commander in Iraq, replacing Gen. George Casey, who would become U.S. Army chief of staff. He also selected Adm. William Fallon to replace Army Gen. John Abizaid, who is retiring as head of U.S. Central Command, the regional headquarters that oversees military operations in the Middle East, including Iraq and Afghanistan. In his next job, Casey would succeed Gen. Peter Schoomaker, who came out of retirement in 2003 to take his current post and has already served longer than the three years traditionally served by Army chiefs of staff. Bush made the nominations, which require confirmation by the Senate, on the recommendation of Defense Secretary Robert Gates. Senate confirmations of military appointments are normally routine. "I firmly believe that Generals Petraeus and Casey and Admiral Fallon, as individuals and as a team, bring to the challenges that face us the qualities necessary to be successful in war and to protect the American people," Gates said in a statement. "I have recommended these three men to the president for these positions because I am convinced they have these talents," he said. White House spokesman Tony Snow said: "The president has accepted these recommendations and will be forwarding these nominations."