The announcement was made this morning.
Prime Minister Jacinda Ardern and her Cook Islands counterpart Mark Brown have instructed officials to continue working together to put in place all measures required to safely recommence two-way quarantine-free travel in the first quarter of next year.
"The arrangement recognises the special ties between New Zealand and the Cook Islands. It will allow people to travel more easily between our two countries, while acknowledging that the priority remains to protect our populations from Covid-19," Ardern said.
Brown welcomed the progress, noting that the free movement of people between New Zealand and the Cook Islands was central to the countries' close relationship and integral to the Cook Islands' recovery from the impact of Covid-19.
"This arrangement is the next step towards resuming many aspects of life in the Cook Islands that have been disrupted by Covid-19, including access to health and education, and reuniting family and friends."
About 80,000 New Zealanders identify as Cook Islanders, according to New Zealand figures, several times the Cook Islands population itself. The Cook Islands is an independent country but its citizens automatically get New Zealand citizenship.
First step now - Cook Island arrivals to skip quarantine
The Cook Island remains one of the few countries around the world and the Pacific region to remain totally free of Covid-19.
As a result, the first step to the new agreement will involve New Zealand officials working to implement a quarantine-free access into New Zealand for anyone travelling from the Cook Islands.
This will be the first time anyone arriving from a different country will not have to carry out the mandatory 14-day managed isolation.
That first step is said to be part of what will be a "phased approach", a statement said.
Ardern said: "Quarantine-free access for travellers from the Cook Islands to New Zealand will provide for the movement of people for delivering essential services, while allowing officials to finalise preparations for a safe return to two-way quarantine-free travel."
Air New Zealand said its teams are busy preparing to start two-way travel between here and the Cooks and is working closely with the government and airports on requirements.
Chief executive Greg Foran said safety will continue being the company's top priority, and it is looking forward to being able to provide people the opportunity to travel again.
Edgewater Resort and Club Raro chief executive Andrew Whittaker said it's huge news as the island has been suffering since the borders have been closed.
He said having some formal agreement in place is an early Christmas present.
"I just think it's great to see. We understand the timeframe that it's taken but as we know it's just getting back to a bit of a new norm really and seeing how we go.
"We're excited about the news today - hopefully we'll hear a bit more about the progress over the next few days and before Christmas."
But National's Covid-19 Response spokesperson Chris Bishop said the Cook Islands bubble was taking too long to set up.
"Today's announcement of 'next steps' in travel between the Cook Islands and New Zealand is an utterly meaningless statement that does no more than repeat that officials are still working on the issue.
"The Prime Minister must explain the delay when a month ago she said there was 'progress' and that it would only take 'a couple of weeks' before a bubble would be up and running once both sides were happy."
- NZ Herald and RNZ