The trainers' flight from Nato base Hohn in Schleswig-Holstein was delayed for several hours when their Transall transport plane broke down.
Another plane had to be found to send the seven trainers on their way.
They will arrive in the Iraqi Kurdish capital of Irbil on Saturday where they will begin training Kurdish troops, who are fighting Islamic terror group Isis, how to use German military equipment.
The Kurds will receive €70-million of used gear from the German military in the next week.
The first shipment includes 4,000 G3 rifles, 4,000 P1 pistols, 20 MILAN anti-tank missile launchers, 120 anti-tank rockets and 20 MG3 machine guns.
But questions remain about the mission and how the trainers will overcome language difficulties. “We don’t know much yet,” one 26-year-old trainer said before departure.
Some of the training will also take place in Germany, with 30 Kurdish soldiers scheduled to arrive in Hammelburg, Bavaria, this month to learn how to use MILAN anti-tank weapons.
France, meanwhile, launched its first air strikes against Isis in Iraq on Friday.