According to Italian media, the badly burnt body was found inside the wreckage of one of the planes, which came down on Tuesday in hilly and wooded countryside near Ascoli Piceno in the Marche region.
The three crew still unaccounted for include Mariangela Valentini, a 31-year-old pilot who had served with NATO forces in Afghanistan and Libya.
According to witnesses, the two planes collided before crashing. It was unclear if any of the crew had been able to eject before impact.
The fighter jets were based at Brescia in northern Italy and had been taking part in training exercises ahead of a larger NATO operation scheduled for later in the year.
An investigation is underway into the cause of the accident.