The prime minister's office said that the $C6 billion ($A6.6 billion) "over-the-horizon" radar system will provide early warning radar coverage from the Canada-United States border into the Arctic.
Carney will make the announcement at a military base in the capital of the Inuit-governed territory of Nunavut.
It is his last stop after visiting Paris and London for meetings with leaders there.
The Australian radar system will consist of a series of pillars about 1.6km in length.
Officials said that the system would have a smaller footprint than what the similar US system would take up.
Senior Canadian government officials, who briefed reporters on Carney's plane before the announcement, said that the purchase has been well received by top military officials in the North American Aerospace Defense Command, the joint US-Canadian military command that overseas threats over the two countries.
But the officials said they could not say how the Australian purchase would be received politically by the US.
The officials spoke on condition of anonymity because they were not authorised to speak publicly.
Carney had earlier had a phone call with Australian Prime Minister Anthony Albanese.
The two leaders discussed global trade and their "commitment to economic co-operation," Australian officials said.
Canada's top military commander will also announce that the government will spend $C420 million to expand Canada's Arctic operations and training exercises and deploy more personnel.
The prime minister is in Iqaluit, which is by far the largest municipality in Nunavut, a vast territory straddling the Arctic Circle.
Nunavut is roughly the size of the US states of Alaska and California combined, with a mostly Inuit population of about 40,000.
