The Bureau of Meteorology said the Hunga Tonga-Hunga Ha'apai volcano erupted at 3.10pm AEDT on Saturday, and tsunami waves have been observed as a result of the eruption.
The bureau said a tsunami wave height of 1.27 metres was observed on Norfolk Island at 9pm AEDT and an 82cm wave was registered on the Gold Coast at 10.54pm AEDT on Saturday.
It said 1.10m-high waves were being recorded at Ned's Beach on Lord Howe Island about 11pm AEDT and a 50cm surge was observed at Hobart's Derwent Park about 11.44pm AEDT.
Port Kembla in NSW's Wollongong registered a 65cm wave at 2.50am AEDT on Sunday.
Countries around the Pacific were also on alert, with the southern Japanese island of Chichijima recording a 75cm wave at 1am AEDT.
The bureau earlier detected a 1.19m wave in Nuku'alofa, Tonga's capital.
A spokesperson for the Australian government said initial assessments are underway and the Department of Foreign Affairs is working to ensure Australians in Tonga are safe and accounted for.
"The size of these waves means the threat is for the marine environment for the east coast of Australia, and for land on Lord Howe Island and Norfolk Island; however the situation will be closely monitored and warnings updated as required," the bureau said in a statement on Saturday night.
"People in land warning zones are strongly advised to move 1 kilometre inland or go to high ground at least 10 metres above sea level.
"While evacuations are not necessary for marine warning zones, people in these areas are advised to leave the water and move away from the immediate water's edge."
The statement said tsunami waves are more powerful than the same size beach waves.
"There will be many waves and the first wave may not be the largest."
Earlier the bureau issued land warnings for Norfolk Island and Lord Howe Island.
Marine warnings are current for all coastal areas of NSW and large parts of the Queensland, Victorian and Tasmanian coasts.
In Queensland the marine warning is in place for Sandy Cape to Point Danger including the Fraser Island coast, Sunshine Coast waters, Moreton Bay and Gold Coast waters.
In Victoria a marine warning is in place from Lakes Entrance to 60 nautical miles east of Gabo Island including the East Gippsland coast.
The marine warning also covers Macquarie Island and parts of Tasmania including the northern tip of Flinders Island to South East Cape, including east of Flinders Island, Banks Strait and Franklin Sound, the upper east coast, the lower east coast, the southeast coast, D'Entrecasteaux Channel, Derwent Estuary, Frederick Henry Bay, Norfolk Bay and Storm Bay.
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