"We feel like family. But just because you feel like family it doesn't mean that the relationship doesn't require effort to work."
She said New Zealand and Australia would be working closely together to stage an "incredibly successful" cup.
"Some of the times that Aussies and Kiwis are talking about sport aren't necessarily the most happy times," Gillard said.
"Coming out of 2011 there have been some moments when we would have wished things had been different.
"But I'm sure that we can leave all that behind us and say today that we are very pleased and proud to be able to work together to deliver the World Cricket Cup."
Local organising committee chairman James Strong presented Gillard and Key with bats signed by the Australian and New Zealand cricket captains, Michael Clarke and Ross Taylor.
The cup will include 14 countries and be broadcast to a potential audience of 953 million people.
Its logo blends Maori and Aboriginal themes: tohara symbolising toughness, pride and tribal culture, and Aboriginal journey tracks symbolising the spirit of the land.