"Four officers have left from Naples. The rest will join them in the next week, from a total group of approximately 45," said a NATO official on Saturday.
"They are going to start straightaway, establish themselves in the Iraqi Ministry of Defence and the General Staff," he said.
"They will concentrate on getting people for training both inside and outside Iraq."
The advance NATO team, due to report back to the allies by 15 September, has been plagued by controversy over whether it should be put under the command of US-led occupation forces.
France, which opposed the invasion and fears this would amount to pushing NATO on to the Iraqi battlefield through the back door, strongly resisted a US push for a "double-hatted" commander who would report both to NATO and a US general.
In the end, the allies decided to leave the decision on the command relationship until mid-September after the return of the advance party, known as the Training Implementation Mission.
The NATO officers are expected to establish liaison arrangements with Iraq's interim government and the occupation force, as well as develop more detailed proposals for NATO training and cooperation.