Mr Marape will attend an official dinner with Prime Minister Anthony Albanese in Canberra before he becomes the first Pacific leader to address parliament.
Mr Marape will use his speech on Thursday to celebrate independence from Australia almost 50 years ago and the relationship that followed.
"There is no greater moment than this for me to go down to Australia and thank them," Mr Marape told reporters before departing Port Moresby.
"We were birthed from the hands of Australia as a nation.
"Our flag was hoisted up and the Australian flag was lowered, not torn down.
"Papua New Guineans must not take our sovereignty for granted - it could have been a different independence."
PNG Foreign Minister Justin Tkatchenko has met with Australian counterparts in Canberra. (Mick Tsikas/AAP PHOTOS)
Mr Marape faces mounting pressure in PNG after deadly riots sparked by the nation's poor economic prospects.
Several members of parliament have resigned and there are calls for a vote of no confidence in his leadership.
Ahead of the visit, PNG Foreign Minister Justin Tkatchenko met with Australian counterparts in Canberra.
While China continues to pursue security ties across the region, Mr Tkatchenko rejected any such deal.
"I want to make this very clear - we are not pressing forward with any security pact or agreement with China, and look forward to implementing the bilateral security arrangement with Australia," he told the ABC.
There's been no revolt from China because we're not supporting their policing policy - they understand clearly where we stand on security in the region and that is with our close traditional partners."
Australia and PNG inked a security pact when Mr Marape last visited in December.
The agreement outlined $200 million to help train PNG police as the Pacific nation aims to almost double the number of officers to 10,000 by 2027.
Australia also continues to mull supporting an NRL team in the Pacific nation.
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