From June 2004 to September 2005 he was in charge of training the new Iraqi army and security forces.
Bush has said that the US army cannot leave Iraq before the Iraqi army is fully trained and manned.
Experience in Mosul
Petraeus commanded the 101st Airborne Division during the 2003 invasion of Iraq and his subsequent administration of the northern city of Mosul was widely praised.
"General Petraeus is an expert in irregular warfare and stability operations [and] ... has been leading the effort to rewrite the military's doctrine for defeating an insurgency," Gates said in a statement.
"He'll bring all the tools to enable Iraqi and coalition forces to create a stable and secure Iraq," Gates.
Casey, 58, would become army chief of staff, he said.
Fallon, 62, nominated to head central command, was a navy combat pilot during the Vietnam war.
During the first Gulf war, he commanded an attack squadron and was involved in Nato's Operation Deliberate Force in Bosnia in 1995.
"As commander of pacific command, Admiral Fallon oversees military operations and security relationships in an area encompassing 43 countries and approximately 60 per cent of the world's population," Gates said.
George Bush, the US president, also announced on Friday that he would move John Negroponte, director of national intelligence, to the state department as deputy to Condoleezza Rice, the US secretary of state.