In his address, Mr Abbott said the Anzac spirit was forged at Gallipoli but crossed many theatres of war and peacekeeping.
That continued to the present day with the joint operation to Iraq due to be deployed soon.
"We remember that we stood together. We always stand together."
He said memorials were not to glorify war, but to remember those who fought for shared values.
Mr Key said it was right that "our closest friend" was first to set up a memorial at the Pukeahu Memorial.
"We like to take the mickey out of each other and we are fierce rivals on the sports field but when it comes to the crunch, we've got each other's backs."
He said the two countries also went to each other's aid in times of need, such as the Canterbury earthquake and Australia's bush fires.
The dedication was also attended by the Defence Force chiefs of both countries - Air Chief Marshall Mark Binskin of the Australian Defence Force and New Zealand's Chief of Defence Force Lieutenant General Tim Keating.
Australia's Veteran Affairs Minister Michael Ronaldson and New Zealand's Veteran's Affairs Minister Maggie Barry also took part.
The Australian memorial was created as part of the new Pukeahu National War Memorial. The $5 million project was funded by the Australian Government and is a reciprocal gesture to the NZ Memorial on Anzac Parade in Canberra.
The Australian memorial features 15 columns of red sand stone, symbolic of the red centre of Australia. Between them are bands of grey stone, symbolising the New Zealand landscape.
The list of battles and wars the Anzac forces served together are inscribed at the memorial, from the Boer War and World War I to Iraq and Afghanistan, as well as peacekeeping missions.
The memorial was designed by Australian architectural firm Tonkin Zulaikha Greer.