The prime minister will sign the Vuvale Union agreement with his Fijian counterpart Sitiveni Rabuka in Suva on Monday - a move that could upgrade ties to a level close to Australia's mutual defence pact with Papua New Guinea.
Mr Albanese arrived in Fiji on Sunday evening, receiving a ceremonial welcome that included an inspection of a guard of honour.
The PukPuk treaty with Port Moresby will come into effect on Wednesday, the same day Mr Albanese is due to meet with his PNG counterpart James Marape.
In an attempt to bolster Australia's key relationships in the region, Mr Albanese will also host the leaders of PNG and Tonga in Brisbane at the final State of Origin game on Wednesday.
"Through one of Australia's favourite sporting codes, we are bringing our Pacific family closer together," Mr Albanese said.
"This important series of meetings in Brisbane comes at a time where we are working closely with our Pacific family on the issues that matter to our region."
Following his visit to Fiji, Mr Albanese will head to the Solomon Islands to meet with his counterpart Matthew Wale after the two nations agreed to further discussions on a security deal.
While visiting Honiara on Tuesday, Mr Albanese will participate in the Solomon Islands' 48th Independence Day celebrations.
The trip follows the sealing of a long-awaited $500 million deal with Vanuatu, called the Nakamal Agreement.
Under the agreement, Port Vila agreed to close the door on foreign military bases in its territory.
The pacts form a key part of an attempt to stave off Chinese influence in the Pacific.
Later in the week, Mr Albanese will travel to Melbourne to meet with Indian Prime Minister Narendra Modi.
Mr Modi will host a major community event at Marvel Stadium on Thursday, with tens of thousands of members of the Indian diaspora expected to attend.
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