Prime Minister Malcolm Turnbull made the announcement in Sydney alongside Indonesian President Joko Widodo.
Both said they were also committed to concluding a free trade deal this year.
The material allegedly ridiculed Indonesia's founding principles, known as Pancasila, and its military.
"President Widodo and I have agreed to full restoration of defence co-operation, training exchanges and activities," Mr Turnbull told a news conference.
Mr Widodo, on his first visit to Australia as head of state, said he was confident that a free trade deal would be finalised this year.
"I have conveyed to Prime Minister Turnbull some of the key issues," he said.
"First is the removal of barriers to trade, tariffs and non-tariffs for Indonesian products such as Indonesia's paper and palm oil."
Earlier this month, Indonesia's military chief said Australia had apologised over the training materials used at an army base in Perth.
Indonesia said the material included "unethical stuff" that discredited Indonesia's military.
Military co-operation between the two nations covers a number of areas, including border control and counter-terrorism.
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