The deal has come under heavy criticism because Malaysia is not a signatory to the United Nations convention on refugees, raising questions about the treatment of the 800 asylum seekers it has agreed to accept.
But Canberra, which is battling to reduce the numbers of boatpeople arriving on its shores, hopes the policy will hurt people smugglers and stop asylum seekers from making the long and dangerous sea journey to Australia.
A Malaysian Home Ministry official said the two countries would sign the deal next Monday in Kuala Lumpur.
He could not immediately give further details, and other officials familiar with the agreement could not immediately be reached.
The Sydney Morning Herald said unnamed sources had revealed that negotiations had secured the support of the United Nations and the deal would be formalised in Kuala Lumpur by ministers from both governments.
A spokesman for Immigration Minister Chris Bowen also said the agreement, which involves Australia taking 4,000 of Malaysia's registered refugees over four years, was imminent.
"It's close, we will be able to say more in coming days," the spokesman told AFP.
More than 500 boatpeople have arrived in Australia since the government announced the Malaysia swap plans in May, and it is not known whether the agreement will apply to them or not.
And as two more boats carrying a combined total of 114 asylum seekers were intercepted Thursday, the government is facing growing unrest at its main detention centre on the remote Indian Ocean territory of Christmas Island.
Conservative opposition leader Tony Abbott, who wants Australia to consider sending boatpeople to the tiny Pacific nation of Nauru for processing, described the Malaysian agreement as "a bad deal".
"I don't think it is going to stop the boats and it is another broken promise from a prime minister who said that she would never send boatpeople to a country that hadn't signed the UN Refugee Convention," he told Channel Nine.