Five bids were received for the army contract, said the Defence Department. It did not name the other bidders.
Work on the contract is scheduled to begin on 1 July.
The new army is expected to reach 12,000 troops within a year and grow to 40,000 within two years.
Vinnell Corporation also trains members of the Saudi National Guard.
The US administrator for occupied Iraq, Paul Bremer, dissolved Iraq’s army last month, leaving tens of thousands of people unemployed.
Old US soldiers to train
On its website, Vinnell said it was seeking former US army and Marine corps officers among others with experience in infantry, mechanized infantry, special forces, special operations, force reconnaissance, maintenance, logistics and supply.
Major General Paul Eaton, former commander of the US infantry centre at Fort Benning, Georgia, will oversee the training.
The new army would initially be a light infantry force, said US military officials.
Vinnell, based in Fairfax, Virginia, is a leader in the growing business of training military forces.