The court, which made its ruling last October, published its written judgement in the case which involved the killing of 203 men, women and children at Arezzo in the central province of Tuscany on June 29, 1944.
The call for compensation arose from the trial in connection with the massacre of former Sergeant Max Josef Milde, 88. He lives in Germany but was condemned to life in jail in absentia.
It was the first time Germany had been ordered at a criminal trial in Italy to pay compensation.
The families of nine of the Arezzo victims had asked for and obtained a total of €800,000 ($1.05 million) in damages from a military court in September 2007.
A lawyer acting for the German government argued unsuccessfully that previous agreements between the two countries had put an end to this type of case.