A fracas broke out between the two countries in January after the material, which apparently involved the West Papua issue and a misspelling of Pancasila, the name for Indonesia's state ideology, was found at a Special Forces base.
Indonesia's military initially responded by cutting all cooperation with Australia, but the government intervened two days later and said the suspension would only affect a language training course.
The Sydney Morning Herald reports that the Australian Army chief, Angus Campbell, has visited Indonesia and conveyed his deep regret and apology over the incident.
The Indonesian military's General Gatot Nurmantyo said the apology had been accepted, but military cooperation would not resume until he had consulted with President Joko Widodo.
Photo: AFP Indonesia's president Joko Widodo